Constraint A: $-3 X_{1}+X_{2} \leq 90$ Constraint B: $4 X_{1}-2 X_{2} \geq 120$ Constraint C: $4 X_{1}+10 X_{2} \leq 40$
All variables are required to be non-negative. Let the objective function be Min: $2 X_{1}-3 X_{2}$. Optimal solution and the corresponding objective function to this problem (assuming the first number in parenthesis is $X_{1}$ and the second number in the parenthesis is $X_{2}$ ) will be
A) $(0,0)$ and 0
B) $(30,0)$ and 60
C) $(54,48)$ and -36
D) $(150,0)$ and 300
E) $(0,90)$ and -270

Question

Quizplus · Accepted Answer

The optimal solution is (54,48) and the corresponding objective function value is -36. This can be found by solving the linear programming problem using the simplex method.

Constraint A −3X1+X2≤90-3 X_{1}+X_{2} \leq 90−3X1​+X2​≤90 Constraint B 4X1−2X2≥1204 X_{1}-2 X_{2} \geq 1204X1​−2X2​≥120

Constraint A $-3 X_{1}+X_{2} \leq 90$ Constraint B $4 X_{1}-2 X_{2} \geq 120$