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"y22", "y2", "x1", "y1", "ox", "oy", "f", "f1", "f0", "f2", "f3", "f4", "f_sorted", "f11", "b2m", "x11", "y11"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve the following Linear Programming problem by applying the geometric method.</p>\n<p><strong>Problem:</strong></p>\n<p style=\"padding-left: 40px;\"><strong>Minimize:</strong>&nbsp; $\\simplify{{ox} x + {oy} y}$</p>\n<p style=\"padding-left: 40px;\"><strong>subject to</strong>:</p>\n<p style=\"padding-left: 80px;\">$\\simplify{-{c21} x - {c22} y &lt;= -{c2}}$</p>\n<p style=\"padding-left: 80px;\">$\\simplify{-{c11} x - {c12} y &lt;= -{c1}}$</p>\n<p style=\"padding-left: 80px;\">$x \\ge \\var{a1} $</p>\n<p style=\"padding-left: 80px;\">$x \\le \\var{a3} $</p>\n<p style=\"padding-left: 80px;\">$y \\le \\var{b2m} $</p>\n<p style=\"padding-left: 80px;\">$x \\ge 0$</p>\n<p style=\"padding-left: 80px;\">$y \\ge 0$</p>\n<p></p>\n<p>The feasible region in this problem is a pentagon with 5 corners. 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