Constraint A: $2 X_{1}+2 X_{2} \leq 14$ Constraint B: $4 X_{1}+10 X_{2} \leq 40$
All variables are required to be non-negative. Let the objective function be Max: $X_{1}+X_{2}$. The optimal solution and the corresponding objective function value to this problem (assuming the first number in parenthesis is $X_{1}$ and the second number in parenthesis is $X_{2}$ ) will be
A) $(0,0)$ and 0
B) $(0,4)$ and 4
C) $(5,2)$ and 7
D) $(0,7)$ and 7
E) C and D

Question

Quizplus · Accepted Answer

The optimal solutions are given by points C $(5,2)$ and D $(0,7)$, both yielding the maximum objective function value of 7. Point C satisfies both constraints and maximizes $X_1 + X_2$ by taking advantage of the available capacity in both constraints. Point D maximizes $X_2$ while $X_1$ is zero, also achieving the maximum value of 7 for the objective function, showing that multiple solutions can exist for linear programming problems.

Constraint A 2X1+2X2≤142 X_{1}+2 X_{2} \leq 142X1​+2X2​≤14 Constraint B 4X1+10X2≤404 X_{1}+10 X_{2} \leq 404X1​+10X2​≤40

Constraint A $2 X_{1}+2 X_{2} \leq 14$ Constraint B $4 X_{1}+10 X_{2} \leq 40$