Question

a. What is the optimal solution in lay terms? What is the optimal value of the objective function?

Variable Cells 12 Cell Name $B$14 DVS values: AM $C$14 DVs values: BM $D$14 DVs values: AP $E$14 DVs values: BP Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 100 0 1.25 1 E+30 6 00 8 1 1.666666667 0 1 .25 14 1E+30 1.25 90 0 91.666666667 1 Constraints Cell Name $B$19 Demand for A $B$20 Demand for B $B$21 Injection-molding time $B$22 Assembly time Final Shadow Value Price 100 12.75 1509 580 0 1080 -0.125 Constraint Allowable R.H. Side Increase 100 11.42857143 150 1E+30 600 1E+30 1080 53.33333333 Allowable Decrease 100 90 20 480

b. Which constraints are binding? Explain.

c. What are the shadow prices of demand for B constraint and assembly time constraints? Interpret each.

d. If you could change the right-hand side of one constraint by one unit (either increase or decrease), which one would you choose? Why? Show all calculations.

e. State and interpret the ranges of optimality for any one of the objective function coefficients.

f. Suppose that the manufacturing cost decreases to $10.45 per case for model A. Would the optimal solution change? Would the optimal objective function value change? Show all calculations.

g. Explain the meaning of reduced cost 1.25 in the sensitivity report. How can you use it?

Answer 1

a. The optimal solution is :

AM=100

BM=60

AP=0

BP=90

The optimal value of objective function=100*12+60*8+0*14+90*9=2490

b.The binding constraints are :

Demand for A,Demand for B and Assembly time.

These constraints are binding because they have no slack value.

c.The shadow price for Demand for B constraint=9

The shadow price for Assembly time constraint=-0.125

A shadow price indicates that by how much the optimal solution changes when the RHS of the constraint is increased by 1 unit.

d.We should choose Demand for A constraint because the shadow price of this constraint is highest and hence the RHS of this constraint should be increased ,as it will have largest increase in the objective function value.

New optimal value =2490+12.75=2502.75