The graph of the feasible region for a mixture problem is shown below. Which of the following profit functions does not have its maximum at the point (6, 6)?
A) P = x + 2y
B) P = 2x + 3y
C) P = x + 3y
D) P = 2x + y

Question

The graph of the feasible region for a mixture problem is shown below. Which of the following profit functions does not have its maximum at the point (6, 6)? 
A) P = x + 2y 
B) P = 2x + 3y 
C) P = x + 3y 
D) P = 2x + y

Quizplus · Accepted Answer

The point (6,6) is the intersection of the lines x=6 and y=6. Evaluating each profit function at this point, we get:

A) P = 6 + 2(6) = 18
B) P = 2(6) + 3(6) = 24
C) P = 6 + 3(6) = 24
D) P = 2(6) + 6 = 18

Therefore, the profit function that does not have its maximum at (6,6) is D, which has a maximum at (6,4).

The Graph of the Feasible Region for a Mixture Problem