optimization-ai999x / figures /lp-two-variable-graphical-region.svg
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<svg class="axp" viewBox="0 0 520 340" role="img" aria-labelledby="axp-optimization-s-0-t" aria-describedby="axp-optimization-s-0-d" xmlns="http://www.w3.org/2000/svg" font-family="system-ui, sans-serif" font-size="12" width="520" height="340"><style>.axp-g{stroke:#8a879466;stroke-width:1}.axp-f{fill:none;stroke:#8a8794}.axp-t{fill:#85828f;font-family:ui-monospace,Menlo,Consolas,monospace;font-size:14px}.axp-l{fill:#7f7c8a;font-size:15px;font-weight:600}.axp-c{fill:none;stroke:#e0306f;stroke-width:2.6;stroke-linejoin:round;stroke-linecap:round}.axp-a{fill:#e0306f1f}.axp-m{fill:#18a874;stroke:#8a8794;stroke-width:1}.axp-d{fill:#e0306f}.axp-mt{fill:#18a874;font-family:ui-monospace,Menlo,Consolas,monospace;font-size:15px;font-weight:600}.axp-c3,.axp-c4{fill:none;stroke-width:2.4;stroke-linejoin:round;stroke-linecap:round}.axp-c3{stroke:#7a5cf0}.axp-c4{stroke:#8a8794;stroke-width:1.8}.axp-b{fill:#e0306f8c}.axp-lt{fill:#7f7c8a;font-size:13px}</style><title id="axp-optimization-s-0-t">A linear programme: feasible region and optimal corner</title><desc id="axp-optimization-s-0-d">Maximise 3x + 5y subject to x ≤ 4; 2y ≤ 12; 3x + 2y ≤ 18, x, y ≥ 0: the feasible region with the corner points the package returns ((0, 0), (0, 6), (2, 6), (4, 0), (4, 3)) and the objective line through the optimum; marked: x = 2, y = 6, objective 36.</desc><clipPath id="axp-optimization-s-0-k"><rect x="78" y="40" width="426" height="238"/></clipPath><line class="axp-g" x1="78.0" y1="40" x2="78.0" y2="278"/><text class="axp-t" x="78.0" y="298" text-anchor="middle">0</text><line class="axp-g" x1="199.7" y1="40" x2="199.7" y2="278"/><text class="axp-t" x="199.7" y="298" text-anchor="middle">2</text><line class="axp-g" x1="321.4" y1="40" x2="321.4" y2="278"/><text class="axp-t" x="321.4" y="298" text-anchor="middle">4</text><line class="axp-g" x1="443.1" y1="40" x2="443.1" y2="278"/><text class="axp-t" x="443.1" y="298" text-anchor="middle">6</text><line class="axp-g" x1="78" y1="278.0" x2="504" y2="278.0"/><text class="axp-t" x="70" y="283.0" text-anchor="end">0</text><line class="axp-g" x1="78" y1="230.4" x2="504" y2="230.4"/><text class="axp-t" x="70" y="235.4" text-anchor="end">2</text><line class="axp-g" x1="78" y1="182.8" x2="504" y2="182.8"/><text class="axp-t" x="70" y="187.8" text-anchor="end">4</text><line class="axp-g" x1="78" y1="135.2" x2="504" y2="135.2"/><text class="axp-t" x="70" y="140.2" text-anchor="end">6</text><line class="axp-g" x1="78" y1="87.6" x2="504" y2="87.6"/><text class="axp-t" x="70" y="92.6" text-anchor="end">8</text><line class="axp-g" x1="78" y1="40.0" x2="504" y2="40.0"/><text class="axp-t" x="70" y="45.0" text-anchor="end">10</text><rect class="axp-f" x="78" y="40" width="426" height="238"/><g clip-path="url(#axp-optimization-s-0-k)"><path class="axp-a" d="M78.0,278.0 L321.4,278.0 L321.4,206.6 L199.7,135.2 L78.0,135.2 Z"/><path class="axp-c" d="M78.0,278.0 L321.4,278.0 L321.4,206.6 L199.7,135.2 L78.0,135.2 Z"/><path class="axp-c4" d="M321.4,278.0 L321.4,40.0" stroke-dasharray="6 4"/><path class="axp-c4" d="M78.0,135.2 L504.0,135.2" stroke-dasharray="6 4"/><path class="axp-c4" d="M78.0,63.8 L504.0,313.7" stroke-dasharray="6 4"/><path class="axp-c3" d="M78.0,106.6 L504.0,206.6"/></g><circle class="axp-d" cx="78.0" cy="278.0" r="4"/><circle class="axp-d" cx="78.0" cy="135.2" r="4"/><circle class="axp-d" cx="199.7" cy="135.2" r="4"/><circle class="axp-d" cx="321.4" cy="278.0" r="4"/><circle class="axp-d" cx="321.4" cy="206.6" r="4"/><circle class="axp-m" cx="199.7" cy="135.2" r="5"/><text class="axp-mt" x="206.9" y="128.0" text-anchor="start">optimum (2, 6)</text><rect class="axp-b" x="78" y="8" width="18" height="11"/><text class="axp-lt" x="102" y="18">feasible region</text><line class="axp-c4" x1="224" y1="14" x2="242" y2="14" stroke-dasharray="6 4"/><text class="axp-lt" x="248" y="18">constraints</text><line class="axp-c3" x1="342" y1="14" x2="360" y2="14"/><text class="axp-lt" x="366" y="18">3x + 5y = 36</text><text class="axp-l" x="291" y="328" text-anchor="middle">x</text><text class="axp-l" transform="translate(18 159) rotate(-90)" text-anchor="middle">y</text></svg>