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Rewriting Linear Programming Problem As Maximization Problem

Question

Rewrite the given linear programming problem as a maximization problem with constraints involving inequalities of the form ≤ (with the exception of the inequalities x ≥ 0, y ≥ 0)

Minimize C = 2x + 3y

Subject to x + y ≤ 9
         x + 2y ≥ 10
         4x + y ≥ 14
         x ≥ 0, y ≥ 0

a. Minimize P = –2x – 3y
Subject to x + y ≤ 12
         x – 2y ≤ –10
         –4x + y ≤ –14
         x ≥ 0, y ≥ 0

b. Minimize P = –2x – 3y
Subject to x + y ≤ 12
         –x – 2y ≤ –10
         –4x – y ≤ 14
         x ≥ 0, y ≥ 0

c. Minimize P = –2x – 3y
Subject to x + y ≤ 12
         –x + 2y ≤ 10
         4x – y ≤ 14
         x ≥ 0, y ≥ 0

d. Minimize P = –2x – 3y
Subject to x + y ≤ 12
         –x – 2y ≤ –10
         –4x – y ≤ –14
         x ≥ 0, y ≥ 0

e. Minimize P = 2x + 3y
Subject to x + y ≤ 12
         x – 2y ≤ –10
         –4x – y ≤ –14
         x ≥ 0, y ≥ 0

Summary

The question belongs to Mathematics and it is about rewriting a linear programming problem as a maximization problem with constraints involving inequalities of the form ≤.

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