{"id":184064,"date":"2022-06-06T15:30:00","date_gmt":"2022-06-06T10:00:00","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=184064"},"modified":"2022-08-20T01:42:25","modified_gmt":"2022-08-19T20:12:25","slug":"graphical-solution-of-linear-programming-problems-cbse-class-12-maths","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/graphical-solution-of-linear-programming-problems-cbse-class-12-maths\/","title":{"rendered":"Graphical Solution of Linear Programming Problems CBSE Class 12 Maths"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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id=\"anim-39396505-8485-45ed-95f8-28c110582946\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.5747126436781609% 0.5747126436781609% 0.5747126436781609% 0.5747126436781609% \/ 2.1739130434782608% 2.1739130434782608% 2.1739130434782608% 2.1739130434782608%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-a2070b2e-1ca3-4dec-b297-67bf154d820a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18836206896551722% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:1.1494252873563218% 2.2988505747126435%;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Graphical Solution of Linear Programming Problems CBSE Class 12 Maths<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:0;width:14.07767%;height:9.38511%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0feb61fc-6088-44b3-ae18-c7c90710d833\">\n<div style=\"position:absolute;width:100%;height:100.00004%;left:0%;top:-0.00002%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png\" alt=\"Aakash Icon Blue PNG\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png 96w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-75x75.png 75w\" sizes=\"(min-width: 1024px) 6vh, 14vw\" 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720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Determinants-11-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Determinants-11-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Determinants-11-150x267.png 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:76.45631%;height:24.75728%;opacity:1\">\n<div id=\"anim-c291b1fa-f411-4d8b-a591-4e74f0a449dc\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-08da62d7-bb4e-43aa-94e6-c5d0b7e70cd4\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.3071895424836601% 1.3071895424836601% 1.3071895424836601% 1.3071895424836601%;background-clip:content-box;background-color:rgba(0,0,0,0.4)\" id=\"el-f132b5e0-e9cf-46e5-8ecb-4865c4fb24d1\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18095238095238048% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:1.2698412698412698% 2.5396825396825395%;color:#000000\"><span><span style=\"color: #edf6f6\">\u2018Linear programming\u2019 is a method to attain the best outcome in a mathematical model whose requirements are expressed by linear relationships.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"ef2601b8-fdf5-4574-b046-06313e4c8c8a\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-2e188d9d-1d0f-4e63-9d9d-634842d27335\",\"keyframes\":[{\"offset\":0,\"transform\":\"translate3d(0, -707.778%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.29,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.45,\"transform\":\"translate3d(0, -199.0271736%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.61,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.71,\"transform\":\"translate3d(0, -67.6635768%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.8,\"transform\":\"translate3d(0, 0%, 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cta-image=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1.png\"><a href=\"https:\/\/byjus-aakash.onelink.me\/GieR\/aakashwebstories\" rel=\"\">Download Aakash APP<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"cf8413e8-8638-4f52-ab50-24cfd17449fa\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-9aae573f-7e2a-4407-8788-7444f451a1f1\",\"keyframes\":{\"transform\":[\"translate3d(114.92064%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-8c4a418c-a1d9-4ef4-ba15-45979cd2eef8\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4df0ee56-35de-46dc-9c8c-ce4a47b52365\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#130406\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-92fc1cb5-be6d-41e0-a44b-8b0a79841ad1\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/46.jpg\" alt=\"46\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/46.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/46-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/46-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/46-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:12.13592%;top:13.26861%;width:76.45631%;height:17.31392%;opacity:1\">\n<div id=\"anim-9aae573f-7e2a-4407-8788-7444f451a1f1\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(114.92064%, 0px, 0)\">\n<div id=\"anim-8c4a418c-a1d9-4ef4-ba15-45979cd2eef8\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-4df0ee56-35de-46dc-9c8c-ce4a47b52365\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.8691588785046727% 1.8691588785046727% 1.8691588785046727% 1.8691588785046727%\" id=\"el-fca7fa23-9bd7-42ac-a7f5-7a5a8a198e26\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.1990476190476187% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Let us see how the solutions for different problems in linear programming are expressed.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:8.25243%;top:26.53722%;width:80.09709%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-c719c66a-2eb0-4313-8b83-da72f01da667\">\n<div style=\"position:absolute;width:100%;height:100.11377%;left:0%;top:-0.05688%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-1-1.png\" alt=\"Graphical-Solution-1-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-1-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-1-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-1-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-1-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"f2f04474-441f-45a1-b97e-75ec8a0c0d41\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-9dbe649d-3160-460a-a87b-386baf548534\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-03b40cfc-9de4-46d5-a06e-27c9b05f9a19\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#0c0819\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-6a5f7407-5db6-4747-9a51-9f5980b182f7\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38.jpg\" alt=\"38\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/38-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:16.66667%;width:80.09709%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f32cbcd6-6d23-40c2-b93a-92ead8023f85\">\n<div style=\"position:absolute;width:100%;height:100.11377%;left:0%;top:-0.05688%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-2-1.png\" alt=\"Graphical-Solution-2-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-2-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-2-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-2-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-2-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:11.48867%;width:76.69903%;height:16.66667%;opacity:1\">\n<div id=\"anim-9dbe649d-3160-460a-a87b-386baf548534\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-03b40cfc-9de4-46d5-a06e-27c9b05f9a19\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.9417475728155338% 1.9417475728155338% 1.9417475728155338% 1.9417475728155338%\" id=\"el-a689135b-4099-460a-b61c-bf51b8a38bb4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18939873417721506% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.339806em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Step 1: List out the given constraints i.e., the general constraints and non-negative constraints.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"43946efa-4942-4387-b717-5a141e0a7118\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-0372d5c6-0119-44c0-9273-ed088919fdc7\",\"keyframes\":{\"opacity\":[1,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-71729d7c-d8cd-4453-8a2e-e0d3d07c4515\",\"keyframes\":{\"transform\":[\"scale(3)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#3f3f41\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f39eaff5-9aa1-454d-bbf3-a1e9576d56e3\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35.jpg\" alt=\"35\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:76.69903%;height:22.16828%;opacity:1\">\n<div id=\"anim-0372d5c6-0119-44c0-9273-ed088919fdc7\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-71729d7c-d8cd-4453-8a2e-e0d3d07c4515\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.4598540145985401% 1.4598540145985401% 1.4598540145985401% 1.4598540145985401%\" id=\"el-e8af8083-4328-4f4f-93c7-55e6a5a6ec3a\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.4525316455696207% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Step 2: Plot the graph for the given constraints and find the feasible region. Let us see how the graph looks for given constraints.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0.24272%;top:12.62136%;width:99.51456%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-75423b1f-d580-4c55-9ec2-9d6f388ac6c7\">\n<div style=\"position:absolute;width:100%;height:124.38376%;left:0%;top:-12.19188%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-4-1.png\" alt=\"Graphical-Solution-4-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-4-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-4-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-4-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-4-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"b23efef2-26d6-41b1-9148-63ed8991b99e\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-96c9ca5a-cc2e-41cd-bd73-f8a5fe2d175c\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-562dc1ef-601a-41a0-9702-d7e2075c93a0\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#323234\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-b9128caf-e453-4048-8667-7d5e18cc7897\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/41.jpg\" alt=\"41\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/41.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/41-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/41-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/41-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:2.18447%;top:12.45955%;width:97.81553%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9d1d04e2-5b86-4e32-9f65-36d34e9401a7\">\n<div style=\"position:absolute;width:100%;height:122.26013%;left:0%;top:-11.13007%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-5-1.png\" alt=\"Graphical-Solution-5-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-5-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-5-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-5-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-5-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 44vh, 98vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:75.97087%;height:27.34628%;opacity:1\">\n<div id=\"anim-96c9ca5a-cc2e-41cd-bd73-f8a5fe2d175c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-562dc1ef-601a-41a0-9702-d7e2075c93a0\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6389776357827476% 0.6389776357827476% 0.6389776357827476% 0.6389776357827476% \/ 1.183431952662722% 1.183431952662722% 1.183431952662722% 1.183431952662722%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-15e26d04-4836-436c-bf0a-c2e9ff0dd2f5\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.17300319488817867% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.307443em;line-height:1.2;text-align:center;padding:1.2779552715654952% 2.5559105431309903%;color:#000000\"><span><span style=\"color: #edf6f6\">Step 3: This step is to identify the coordinates of the feasible region that we get from&nbsp;<\/span><br \/>\n<span style=\"color: #edf6f6\">step 2. For the given example, we see that (1, 2) is the coordinate for the feasible region.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"5f6d4ac7-d449-4eac-b768-878108025ca3\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-0a557ad6-5d44-4e29-8cdc-400177b76fed\",\"keyframes\":{\"opacity\":[1,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-724fc05d-00de-4a8f-8bac-5aba4f5bd37c\",\"keyframes\":{\"transform\":[\"scale(3)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#041b1f\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-b145ddf9-7733-46b8-99c5-270648dfd68e\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/51.jpg\" alt=\"51\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/51.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/51-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/51-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/51-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:76.69903%;height:16.99029%;opacity:1\">\n<div id=\"anim-0a557ad6-5d44-4e29-8cdc-400177b76fed\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-724fc05d-00de-4a8f-8bac-5aba4f5bd37c\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.9047619047619049% 1.9047619047619049% 1.9047619047619049% 1.9047619047619049%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-00d57aa2-6e0c-4ba1-84de-4405a10af2b4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18037974683544256% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #edf6f6\">Step 4: See what is being asked in the problem. Is it to maximize the given linear program or to minimize it?<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-0.24272%;top:12.78317%;width:100.48544%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-c477e0f4-110d-4064-88b0-0be534f59a2c\">\n<div style=\"position:absolute;width:100%;height:125.59727%;left:0%;top:-12.79863%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-6-1.png\" alt=\"Graphical-Solution-6-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-6-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-6-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-6-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-6-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"88eeca4b-25e3-4d7d-813b-dfaf8ce894c7\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-241ed00b-bd84-4d1b-a304-26206c483a80\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ad9e86d9-7d4a-4756-839c-8e755018cf17\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#1e2532\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-eb55a770-5e83-4690-8612-f8b3933f83f0\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/52.jpg\" alt=\"52\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/52.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/52-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/52-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/52-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:7.76699%;top:11.32686%;width:76.69903%;height:15.69579%;opacity:1\">\n<div id=\"anim-241ed00b-bd84-4d1b-a304-26206c483a80\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-ad9e86d9-7d4a-4756-839c-8e755018cf17\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 2.0618556701030926% 2.0618556701030926% 2.0618556701030926% 2.0618556701030926%\" id=\"el-2b39d9fc-633c-4f03-a1c9-ea1371ba1da4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.17136075949367063% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.307443em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Substitute all intersecting points on the graph to the given linear program to find the maximum or minimum values.&nbsp;<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:32.8479%;width:80.09709%;height:78.64078%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-4a0e8075-fd27-4705-b917-01ff8616e968\">\n<div style=\"position:absolute;width:100%;height:120.7133%;left:0%;top:-20.62136%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-8-1-1.png\" alt=\"Graphical-Solution-8-1 (1)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-8-1-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-8-1-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-8-1-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-8-1-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"e8888924-b175-4112-99b3-7e04c1bf9939\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e19c3059-cffa-4384-be69-c4ee2dcff400\",\"keyframes\":{\"opacity\":[1,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5e579e19-4dee-440b-93c9-8cc83836b595\",\"keyframes\":{\"transform\":[\"scale(3)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#131c30\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9dcd8233-04e8-4e5b-b11a-57bd4227f180\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/53.jpg\" alt=\"53\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/53.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/53-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/53-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/53-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:2.18447%;top:11.65049%;width:97.81553%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-51460b91-2c8d-4473-b13c-0440fa3efd0c\">\n<div style=\"position:absolute;width:100%;height:122.26013%;left:0%;top:-11.13007%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-7-1.png\" alt=\"Graphical-Solution-7-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-7-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-7-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-7-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-7-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 44vh, 98vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:76.69903%;height:13.1068%;opacity:1\">\n<div id=\"anim-e19c3059-cffa-4384-be69-c4ee2dcff400\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-5e579e19-4dee-440b-93c9-8cc83836b595\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 2.4691358024691357% 2.4691358024691357% 2.4691358024691357% 2.4691358024691357%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-02667485-8541-4cf3-8aee-269f56316bae\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18037974683544256% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #edf6f6\">Hence the given function is maximum at (0,3) and minimum at (0,0).<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"feb509bf-ec63-4311-a23c-af61c07855d3\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-39e98450-63fa-4694-89c8-167bd16fbedd\",\"keyframes\":{\"opacity\":[1,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-4c706e42-b131-43db-819b-766ffc68a364\",\"keyframes\":{\"transform\":[\"scale(3)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#241305\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ab217238-df0e-4609-a4e5-514d515acb7e\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/16.jpg\" alt=\"16\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/16.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/16-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/16-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/16-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:18.60841%;width:100%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-1ce6233b-73e9-4d4a-a358-ffd870aa19e5\">\n<div style=\"position:absolute;width:100%;height:124.99051%;left:0%;top:-12.37858%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-9-1.png\" alt=\"Graphical-Solution-9-1\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-9-1.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-9-1-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-9-1-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Graphical-Solution-9-1-150x267.png 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:76.69903%;height:21.0356%;opacity:1\">\n<div id=\"anim-39e98450-63fa-4694-89c8-167bd16fbedd\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-4c706e42-b131-43db-819b-766ffc68a364\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.5384615384615385% 1.5384615384615385% 1.5384615384615385% 1.5384615384615385%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-e8f3205f-bfa4-49d0-a4c8-23cded1daaf4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18037974683544256% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #edf6f6\">Let us see another example of graphical solutions.<\/span><br \/>\n<span style=\"color: #edf6f6\">Minimize B = -3x+4y subject to x+2y\u22648 and&nbsp;<\/span><br \/>\n<span style=\"color: #edf6f6\">3x+2y\u226412, x, y \u22650<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"3d92db2d-173c-4ad9-b49e-65f8d875f3c6\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-f3f9fe03-5fc1-4f1c-93af-eb231a0801ec\",\"keyframes\":{\"opacity\":[1,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e48ac307-b677-45f0-8086-305c496b8307\",\"keyframes\":{\"transform\":[\"scale(3)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#b6b5ba\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-4fd6887e-9be5-4a13-b636-1b7c41386fb5\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-6.jpg\" alt=\"share-6\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-6.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-6-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-6-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/share-6-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:10.43689%;top:76.53722%;width:76.69903%;height:24.75728%;opacity:1\">\n<div id=\"anim-f3f9fe03-5fc1-4f1c-93af-eb231a0801ec\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:none\">\n<div id=\"anim-e48ac307-b677-45f0-8086-305c496b8307\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(3)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.3071895424836601% 1.3071895424836601% 1.3071895424836601% 1.3071895424836601%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-ac28af18-77d5-40c5-89db-d3d790859444\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.18037974683544256% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.323625em;line-height:1.2;text-align:center;padding:1.2658227848101267% 2.5316455696202533%;color:#000000\"><span><span style=\"color: #edf6f6\">Hope you have got the idea of finding graphical solutions for given linear programming. Now, share these with your friends and help them to score well.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u2018Linear programming\u2019 is a method to attain the best outcome in a mathematical model whose requirements are expressed by linear relationships.<\/p>\n","protected":false},"author":1,"featured_media":184122,"template":"","meta":{"web_stories_publisher_logo":224645,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[],"web_story_tag":[],"class_list":["post-184064","web-story","type-web-story","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Graphical Method of Linear Programming Problems CBSE Class 12 Maths<\/title>\n<meta name=\"description\" content=\"Graphical Method of Linear Programming: Graphical Method is the most basic method to solve Linear Programming Problems by finding the Optimum Point. Let us see how solve linear Programming problems in graphical method on aakash.ac.in\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aakash.ac.in\/blog\/web-stories\/graphical-solution-of-linear-programming-problems-cbse-class-12-maths\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Graphical Method of Linear Programming Problems CBSE Class 12 Maths\" \/>\n<meta property=\"og:description\" content=\"Graphical Method of Linear Programming: Graphical Method is the most basic method to solve Linear Programming Problems by finding the Optimum Point. 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