Consider the following constraints from a two-variable Linear Program.
(1) X ≥ 0
(2) Y ≥ 0
(3) X + Y ≤ 20
(4) 2X + 5Y ≤ 70
If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?
A) (0, 20)
B) (20, 0)
C) (10, 10)
D) (0, 14)
E) (35, 0)

Question

Quizplus · Accepted Answer

Constraints (3) and (4) are binding, which means they hold with equality at the optimal solution. Solving for (3) and (4) simultaneously, we get X=10 and Y=10, which satisfies constraints (1) and (2) as well. Therefore, the optimal solution is (10, 10) and the correct answer is choice C.

Consider the Following Constraints from a Two-Variable Linear Program