Constraint A: $3 X_{1}+X_{2} \geq 90$ Constraint B: $3 X_{1}+2 X_{2} \leq 120$ Constraint C: $X_{1}-X_{2} \geq 0$
All variables are required to be non-negative. Let the objective function be Max: $X_{1}+X_{2}$ Non-binding constraint corresponding to the optimal solution in this problem will be
A) constraint A
B) constraint B
C) constraint $\mathrm{C}$
D) both $\mathrm{A}$ and $\mathrm{B}$
E) no redundant constraint

Question

Quizplus · Accepted Answer

Constraint B is non-binding because the objective function seeks to maximize $X_{1}+X_{2}$, and constraints A and C together ensure that $X_{1}$ is at least as large as $X_{2}$ and that their combination is pushed towards higher values. Constraint B, which limits the sum of $3X_{1}+2X_{2}$, is less likely to be the limiting factor in maximizing $X_{1}+X_{2}$ because it allows for a larger combination of $X_{1}$ and $X_{2}$ than constraint A does, making it non-binding or redundant in the context of maximizing the objective function.

Constraint A 3X1+X2≥903 X_{1}+X_{2} \geq 903X1​+X2​≥90 Constraint B 3X1+2X2≤1203 X_{1}+2 X_{2} \leq 1203X1​+2X2​≤120

Constraint A $3 X_{1}+X_{2} \geq 90$ Constraint B $3 X_{1}+2 X_{2} \leq 120$