Consider the following constraints from a two-variable Linear Program.
(1) X ≥ 0
(2) Y ≥ 0
(3) 10X + 4Y ≤ 110
(4) 5X - Y ≤ 40
If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?
A) (11, 0)
B) (0, 27.5)
C) (0, -40)
D) (9, 5)
E) not enough information is provided to answer the problem

Question

Quizplus · Accepted Answer

Since constraints (3) and (4) are binding, we can rewrite them as equalities:
10X + 4Y = 110
5X - Y = 40
Solving these two equations simultaneously gives X = 9 and Y = 5, which satisfies the non-negativity constraints (1) and (2). Therefore, the optimal solution is (9, 5).

Consider the Following Constraints from a Two-Variable Linear Program