Maximise (or minimise) a linear objective subject to linear inequality constraints. The optimum sits at a corner of the feasible region.
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Maximise z = 3x + 2y subject to x+y ≤ 4, x,y ≥ 0
Corners: (0,0), (4,0), (0,4). z values: 0, 12, 8. Max at (4, 0): z = 12.