The binding constraints for this problem are the first and second.
Min $\mathrm { x } _ { 1 } + 2 \mathrm { x } 2$
s.t.
$x _ { 1 } + x _ { 2 } \geq 300$
$2 \mathrm { x } _ { 1 } + \mathrm { x } _ { 2 } \geq 400$
$2 \mathrm { x } 1 + 5 \mathrm { x } _ { 2 } \leq 750$
$\mathrm { x } _ { 1 } , \mathrm { x } _ { 2 } \geq 0$
a.Keeping c₂ fixed at 2,over what range can c₁ vary before there is a change in the optimal solution point?
b.Keeping c₁ fixed at 1,over what range can c₂ vary before there is a change in the optimal solution point?
c.If the objective function becomes Min 1.5x₁ + 2x₂,what will be the optimal values of x₁,x₂,and the objective function?
d.If the objective function becomes Min 7x₁ + 6x₂,what constraints will be binding?
e.Find the dual price for each constraint in the original problem.

Question

The binding constraints for this problem are the first and second.
Min

\mathrm { x } _ { 1 } + 2 \mathrm { x } 2

s.t.

x _ { 1 } + x _ { 2 } \geq 300

2 \mathrm { x } _ { 1 } + \mathrm { x } _ { 2 } \geq 400

2 \mathrm { x } 1 + 5 \mathrm { x } _ { 2 } \leq 750

\mathrm { x } _ { 1 } , \mathrm { x } _ { 2 } \geq 0

a.Keeping c₂ fixed at 2,over what range can c₁ vary before there is a change in the optimal solution point?
b.Keeping c₁ fixed at 1,over what range can c₂ vary before there is a change in the optimal solution point?
c.If the objective function becomes Min 1.5x₁ + 2x₂,what will be the optimal values of x₁,x₂,and the objective function?
d.If the objective function becomes Min 7x₁ + 6x₂,what constraints will be binding?
e.Find the dual price for each constraint in the original problem.

Quizplus · Accepted Answer

The Answer of The binding constraints for this problem are the first and second. Min $\mathrm { x } _ { 1 } + 2 \mathrm { x } 2$ s.t. $x _ { 1 } + x _ { 2 } \geq 300$ $2 \mathrm { x } _ { 1 } + \mathrm { x } _ { 2 } \geq 400$ $2 \mathrm { x } 1 + 5 \mathrm { x } _ { 2 } \leq 750$ $\mathrm { x } _ { 1 } , \mathrm { x } _ { 2 } \geq 0$ a.Keeping c₂ fixed at 2,over what range can c₁ vary before there is a change in the optimal solution point? b.Keeping c₁ fixed at 1,over what range can c₂ vary before there is a change in the optimal solution point? c.If the objective function becomes Min 1.5x₁ + 2x₂,what will be the optimal values of x₁,x₂,and the objective function? d.If the objective function becomes Min 7x₁ + 6x₂,what constraints will be binding? e.Find the dual price for each constraint in the original problem.

The Binding Constraints for This Problem Are the First and Second