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In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint?
$\begin{array} { l l }
\text { Maximize } P = 3 x + 15 y \
\text { subject to } & 2 x + 4 y \leq 12 \
& 5 x + 2 y \leq 10 \
\text { and } \quad x \geq 0 , y \geq 0
\end{array}$
A) 8
B) 10
C) 12
D) 15
E) ? (infinity)

Question

Note: This question requires access to Solver.
In the following linear programming problem, what is the allowable increase in the right-hand side of the first constraint?
$\begin{array} { l l } 
\text { Maximize } P = 3 x + 15 y \
\text { subject to } & 2 x + 4 y \leq 12 \
& 5 x + 2 y \leq 10 \
\text { and } \quad x \geq 0 , y \geq 0
\end{array}$
A) 8
B) 10
C) 12
D) 15
E) ? (infinity)

Quizplus · Accepted Answer

The allowable increase in the right-hand side of the first constraint is the amount by which the objective function can be increased without changing the optimal solution. In this case, the optimal solution is x = 2 and y = 1, and the objective function value is P = 3(2) + 15(1) = 21. If the right-hand side of the first constraint is increased by 8, the new constraint will be 2x + 4y ≤ 20, and the optimal solution will still be x = 2 and y = 1. The objective function value will increase to P = 3(2) + 15(1) = 29. Therefore, the allowable increase in the right-hand side of the first constraint is 8.

Note: This Question Requires Access to Solver A) 8 B) 10 C) 12 D) 15 E)

Note: This Question Requires Access to Solver A) 8
B) 10
C) 12
D) 15
E)