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TVGuru Inc. manufactures LCD TV and Plastma TV sets in its kentucky plant. The c

ID: 3355537 • Letter: T

Question

TVGuru Inc. manufactures LCD TV and Plastma TV sets in its kentucky plant. The company makes a profit of $400 on each Plasma TV and $300 on each LCD TV set. The production process has a capacity of 30,000 machine-hours. It takes 3 machine-hoursto a produce a unit of Plasma TV and 1 machine-hour to produce a unit of LCD TV. After market research survey by a well-known research firm, it is concluded that no more than 8,000 Plasma and 12,000 LCD TVs could be sold.

A. Formulate the LP model.

Using solver output and sensitivity reports, answer the following

B. -What is the optimal product mix?

-What is the maximum profit?

C. Capacity can be increased by 1,000 machine-hours for a cost of $100,000. Should the company increase the capacity?

D. There was an error in the market research report and the actual demand for Plasma TV is less than 8,000.

-If demand is 6,000 would it change the optimum solution?

-What if demand was 5,000?

Explanation / Answer

Here lets say there are X units of LCD TV and Y units of Plasma TV is made.

Total profit

TP = 300 X + 400Y

Constraints are :

X + 3Y = 30000

Y < = 8000

X < = 12000

(B) Here by using solver output and sensitivity reports

we get optimal products mix is :

X = 12000

Y = 6000

Maximum profit = 300 * 12000 + 6000 * 400 = 6000000

(C) If capicity is increased by 1000 machine hours then optimum mix

X = 12000 and Y = 6333.33

Total profit = 300 * 12000 + 6333.33 * 400 = $ 6133333

Cost = $ 100,000

Total additional profit = $ 6133333 - $ 6000000 = $ 133333

so the company shall increase the capacity.

(D) If demand of plasma TV is 6000 maximum then the optimal solution will not change as it would be the same.

(ii) but if demand was 5000, then it would change. new optimal mix is

X = 12000 and Y = 5000