Practice Linear Programming in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Linear programming optimizes a linear objective subject to linear inequality or equality constraints.

You search the corners of an allowed region for the best score.

Example 1

medium
Maximize z = 3x + 2y subject to x + y \leq 4, x \geq 0, y \geq 0.

Example 2

hard
Minimize z = 2x + 5y subject to x + 2y \geq 6, x + y \geq 4, x \geq 0, y \geq 0.

Example 3

easy
A feasible region has vertices at (0,0), (5,0), (3,4), (0,6). Maximize z = x + 2y.

Example 4

medium
A company makes chairs (\40 profit) and tables (\70 profit). Each chair takes 2 hours, each table takes 5 hours. With 40 hours available, maximize profit.
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