Question

The Electrotech Corporation manufactures two industrial-sized devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires 2 hours of wiring and 1 hour of testing and can be sold for $250 profit. Each alternator requires 3 hours of wiring and 2 hours of testing and can be sold for a $150 profit. There are 260 hours of wiring time and 140 hours of testing time available in the next production period and Electrotech would like to maximize profit. Use Solver to create Answer and Sensitivity Reports.

A. How much excess wiring and testing capacity exists in the optimal solution?

B. What is the company’s total profit if it has 10 additional hours of wiring capacity?

C. By how much does the profit on alternators needs to increase before their production is justified?

D. Does the optimal solution change if the marginal profit on generators decreases by $50 and the marginal profit on alternators increases by $75?

E. Suppose the marginal profit on generators decreases by $25. What is the maximum profit that can be earned on alternators without changing the optimal solution?

F. Suppose the amount of wiring required on alternators is reduced to 1.5 hours. Does this change the optimal solution? Why or why not?

Answer 1

SOLUTION:-

LP model for this problem is

a) by using graph for constraints to find corner points

A(0,70)
B(100,20)
C(130,0)
satisfies the constraints So these are the corner points
Z at A=> Z(0,70)=250*0+150*70=10500
Z at B => Z(100,20)=250*100+150*20=28000
Z at C=> Z(130,0)=250*130+150*0=32500

So at C(130,0) it has maximum value so 130 generators used
So working hours used=260
and testing capacity exists=130

excess=130

b)

10 Additional wiring capacity added

therefore

Same as above

A(0,70)
B(120,10)
C(135,0)
satisfies the constraints So these are the corner points
Z at A=> Z(0,70)=250*0+150*70=10500
Z at B => Z(100,20)=250*120+150*10=31500
Z at C=> Z(130,0)=250*135+150*0=33750

So at C(135,0) it has maximum value so 135 generators used
So working hours used=270
and testing capacity exists=135

d)

It decrease because its only depend on generators only

e)

Maximum profit=$225*130=$29250