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: $X_{1}+X_{2}$ The optimal solution (assuming the first number in parenthesis is $X_{1}$ and the second number in the parenthesis is $X_{2}$ ) will be
A) $(24,24)$
B) $(0,60)$
C) $(20,30)$
D) $(22.5,22.5)$
E) $(0,90)$

Question

Quizplus · Accepted Answer

The optimal solution is (24, 24) because it satisfies all the constraints and maximizes 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 $3 X_{1}+2 X_{2} \leq 120$