What is the optimal solution (X, Y, Z) to the following linear program?
Max 2X + 4Y + 6Z
Subject to
Z ≤ 0
X + Y + Z ≤ 20
X, Y, Z ≥ 0
A) (0, 0, 20)
B) (20, 0, 0)
C) (0, 20, 0)
D) (20, 20, 20)
E) the solution is unbounded

Question

Quizplus · Accepted Answer

The constraint Z ≤ 0 means that Z can only be 0 or negative. Since we want to maximize the objective function, we want to set Z to be as small as possible (i.e., 0).

So the constraints become:
X + Y ≤ 20
X, Y ≥ 0

Now we can maximize the objective function of 2X + 4Y + 6Z. 
Substituting Z = 0:
Max 2X + 4Y

We can graph this linear program and find that the optimal solution (intersection of the two lines) is at (0, 20, 0). Therefore, the answer is C.

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