In a linear programming problem, the binding constraints for the optimal solution are:
5x1 + 3x2 ≤ 30
2x1 + 5x2 ≤ 20
Which of these objective functions will lead to the same optimal solution?
A) 2x1 + 1x2
B) 7x1 + 8x2
C) 80x1 + 60x2
D) 25x1 + 15x2

Question

Quizplus · Accepted Answer

The optimal solution will occur at the intersection of the two binding constraints, which is (x1, x2) = (3, 2). Plugging this into the objective function options, we can calculate the optimal value:
Option A: 2x1 + 1x2 = 2(3) + 1(2) = 8
Option B: 7x1 + 8x2 = 7(3) + 8(2) = 35
Option C: 80x1 + 60x2 = 80(3) + 60(2) = 420
Option D: 25x1 + 15x2 = 25(3) + 15(2) = 105

Option D gives the smallest optimal value, which means it will lead to the same optimal solution as the objective function in the original problem.

In a Linear Programming Problem, the Binding Constraints for the Optimal