{"id":988,"date":"2024-10-28T12:14:59","date_gmt":"2024-10-28T04:14:59","guid":{"rendered":"https:\/\/www.math.ntnu.edu.tw\/merc\/?page_id=988"},"modified":"2025-10-23T11:21:44","modified_gmt":"2025-10-23T03:21:44","slug":"linearprogramming","status":"publish","type":"page","link":"https:\/\/www.math.ntnu.edu.tw\/merc\/animated_math\/linearprogramming\/","title":{"rendered":"\u7528\u7dda\u6027\u898f\u5283\u8cfa\u66f4\u591a\u9322"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"988\" class=\"elementor elementor-988\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3fb16c93 e-flex e-con-boxed e-con e-parent\" data-id=\"3fb16c93\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-498bce2c elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"498bce2c\" data-element_type=\"widget\" data-e-type=\"widget\" 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elementor-size-default\">\u7528\u7dda\u6027\u898f\u5283\u8cfa\u66f4\u591a\u9322<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1fb3ae0c e-flex e-con-boxed e-con e-parent\" data-id=\"1fb3ae0c\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-25c83c94 elementor-widget elementor-widget-video\" data-id=\"25c83c94\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u7528\u7dda\u6027\u898f\u5283\u8cfa\u66f4\u591a\u9322.mov\" autoplay=\"\" loop=\"\" controls=\"\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-36661f06 e-flex e-con-boxed e-con e-parent\" data-id=\"36661f06\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-17ff4c8a elementor-widget elementor-widget-text-editor\" data-id=\"17ff4c8a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div>\n\u4f60\u7ba1\u7406\u5169\u7a2e\u7522\u54c1\uff0c\u7522\u54c1 A \u548c\u7522\u54c1 B\uff0c\n\u7522\u54c1 A \u6bcf\u55ae\u4f4d\u7684\u5229\u6f64\u70ba ${\\rm $}0.50$\uff0c\u7522\u54c1 B \u6bcf\u55ae\u4f4d\u7684\u5229\u6f64\u70ba ${\\rm $}1.00$\u3002\n\u4f60\u60f3\u8981\u6700\u5927\u5316\u7e3d\u5229\u6f64 P\u3002<\/div>\n<div>$P=0.5A+B$<\/div>\n<div>\u7136\u800c,\u9700\u8981\u6eff\u8db3\u4ee5\u4e0b\u9650\u5236\u689d\u4ef6:\n\u7531\u65bc\u6750\u6599\u9650\u5236,\u751f\u7522\u7684\u7e3d\u55ae\u4f4d\u6578(\u5169\u7a2e\u7522\u54c1\u5408\u8a08)\u4e0d\u80fd\u8d85\u904e 6 \u500b\u55ae\u4f4d\u3002<\/div>\n<div>$A+B \\leq 6$<\/div>\n<div>\u7531\u65bc\u5e02\u5834\u9700\u6c42,\u7522\u54c1 A \u548c\u7522\u54c1 B \u7684\u55ae\u4f4d\u6578\u91cf\u5dee\u7570\u4e0d\u61c9\u8d85\u904e 2 \u500b\u55ae\u4f4d\u3002<\/div>\n<div>$A-B \\leq 2$<\/div>\n<div>$B-A \\leq 2$<\/div>\n<div>\u5169\u7a2e\u7522\u54c1\u7684\u751f\u7522\u6578\u91cf\u90fd\u4e0d\u80fd\u70ba\u8ca0\u6578\u3002<\/div>\n<div>$A,B \\geq 0$<\/div>\n<div>$${\\rm \u6700\u5927\u5316} \\ P=0.5A+B$$\n$${\\rm \u9650\u5236\u689d\u4ef6\u70ba} \\ A+B \\leq 6, A-B \\leq 2, B-A \\leq 2, A,B \\geq 0$$<\/div>\n<div>\u6700\u5927\u5229\u6f64\u70ba $5.00\u3002<\/div>\n<div style=\"margin-top: 20px;\"><a style=\"font-size: 32; color: red;\" href=\"https:\/\/www.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u7528\u7dda\u6027\u898f\u5283\u8cfa\u66f4\u591a\u9322.pdf\" target=\"_blank\" rel=\"noopener\">\u5b78\u7fd2\u55ae\uff1a\u7528\u7dda\u6027\u898f\u5283\u8cfa\u66f4\u591a\u9322\u5b78\u7fd2\u55ae<\/a><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-7e17cca4 e-flex e-con-boxed e-con e-parent\" data-id=\"7e17cca4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4ac325a8 elementor-widget elementor-widget-text-editor\" data-id=\"4ac325a8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div 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