Constraint A: $-2 X_{1}+2 X_{2} \geq 14$ Constraint B: $4 X_{1}+10 X_{2} \leq 40$ All variables are required to be non-negative. Let the objective function be Max: $2 X_{1}+3 X_{2}$. 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 18
C) problem is infeasible
D) solution is unbounded
E) $(10,0)$ and 20

Question

Quizplus · Accepted Answer

The problem is infeasible because the constraints cannot be satisfied simultaneously. Constraint A requires $X_2 \geq 7 + X_1$, while Constraint B limits $X_2 \leq 4 - 0.4X_1$. These conditions cannot be met together for non-negative values of $X_1$ and $X_2$.

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

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