Suppose that a maximization LP problem has corners of (0,0), (5,0), and (0,5). How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X+5Y?
A) 0
B) 1
C) 2
D) 5
E) Infinite

Question

Quizplus · Accepted Answer

Given the profit function 5X + 5Y, any combination of X and Y along the line connecting (5,0) and (0,5) will yield the same maximum profit because the profit function is linear and the coefficients of X and Y are equal. This means that as long as the sum of X and Y equals 5, the profit will be maximized, resulting in an infinite number of combinations along that line.

Suppose That a Maximization LP Problem Has Corners of (0,0)