The Binding Constraints for This Problem Are the First and Second

question 44

Essay

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.

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Definitions:

Direct Materials Purchases Variance

This term refers to the difference between the actual cost of materials purchased and the expected (standard) cost of materials needed to manufacture the products during a specific period.

Materials Price Variance

The difference between the actual cost of materials and the expected (standard) cost.

Raw Material

The basic material from which a product is made, used in the initial stages of production.

Materials Price Variance

The difference between the actual cost of materials and the standard cost multiplied by the quantities purchased.