Linear Programming Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

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

Solution

  1. 1
    z(0,0)=0z(0,0)=0, z(5,0)=5z(5,0)=5, z(3,4)=11z(3,4)=11, z(0,6)=12z(0,6)=12.
  2. 2
    Maximum: z=12z = 12 at (0,6)(0, 6).

Answer

z=12z = 12 at (0,6)(0, 6)
Evaluate the objective function at each vertex and pick the largest value. No calculus needed — linear functions over polygons always achieve their extremes at corners.

About Linear Programming

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

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More Linear Programming Examples

Example 1 medium

Maximize [formula] subject to [formula], [formula], [formula].

Example 2 hard

Minimize [formula] subject to [formula], [formula], [formula], [formula].

Example 4 medium

A company makes chairs ([formula]40[formula][formula] profit). Each chair takes 2 hours, each table

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