Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $3Y what is the maximum profit the company can earn?
A) $0
B) $10
C) $15
D) $14
E) $21

Question

Quizplus · Accepted Answer

We can graph the feasible region and then evaluate the profit at each corner point to find the maximum.

To graph the feasible region, we plot the four corner points and connect them with lines:

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Since we are maximizing $X + $3Y, we want to find the corner point that gives us the highest value for this expression. We evaluate this expression at each corner point and find that:

- (0,0) gives us $0
- (10,0) gives us $10
- (5,5) gives us $20
- (0,7) gives us $21

Therefore, the maximum profit the company can earn is $21, which is achieved at point (0,7). The answer is E.

Suppose That the Feasible Region of a Maximization LP Problem