An electronic company is considering the production of four products : MP3 playe

Question

An electronic company is considering the production of four products : MP3 players, Satellite radio tuners, LCD TVs, and DVD players. For sake of simplicity assume that input for all products can viewed in terms of just three resources: electronic components, non-electronic components, and assembly times. The composition of four products in terms of these three inputs , profit per unit and resource supplies are given in table below :

Company is interested to know how many of each product to produce while maximizing the profit.

Algebraic formulation

Objective function Maximize profit = $29M + $32S + $72T + $54B

subject to 3M + 4S + 4T + 3B 4,700 (electronic components)

2M + 2S + 4T + 3B 4,500 (nonelectronic components)

M + S + 3T + 2B 2,500 (assembly line time, hrs)

M, S, T, B 0 (nonnegativity)

1. How many of each of the 4 electronic products should the company produce?

2. What is the maximum profit?

3. Are there any leftover resources? What are they and how much?

4. What would be the impact on profit if the supply of nonelectrical components changes?

5. What would be the impact on profit if the supply of electrical components increased by 400 units (to a total of 5100)?

6. What would be the impact on profit if the supply of electrical components increased by 4000 units (to a total of 8700)? 25

7.What would happen if we could buy an additional 400 elec. components for $1 per component? Would we want to buy them? Why or why not?

8.What if we could get an additional 250 hours of assembly time by paying $5 per hour ? Would this be profitable? Why or why not?

9.For what range of profit contributions for DVD players will the current solution remain optimal?

10.What happens to profit if this value drops to $50 per DVD player?

MP3 Player Satellite Radio Tuner LCD TV Blue ray DVD player Supply Electronics components 3 4 4 3 4700 Non - Electronics components 2 2 4 3 4500 Assembly time - hours 1 1 3 2 2500 Profit per unit $29 $32 $72 $54

Explanation / Answer

1. How many of each of the 4 electronic products should the company produce?

Mp3=0, Satellite radio=380, LCD=0, Blue Ray=1060

2. What is the maximum profit?

$69400

3. Are there any leftover resources? What are they and how much?

Yes, Non - Electronics components is left by 560 others are utilized

4. What would be the impact on profit if the supply of nonelectrical components changes?

Up to 560 units the supply can go down and there won’t be any changes on profit.

5. What would be the impact on profit if the supply of electrical components increased by 400 units (to a total of 5100)?

Profit would increase to $70200.

6. What would be the impact on profit if the supply of electrical components increased by 4000 units (to a total of 8700)? 25

Profit would increase to $75000

7.What would happen if we could buy an additional 400 elec. components for $1 per component? Would we want to buy them? Why or why not?

Yes we would want to buy them because we will have an additional $800 profit while incurring a cost of $400 only.

8.What if we could get an additional 250 hours of assembly time by paying $5 per hour ? Would this be profitable? Why or why not?

Yes it will be profitable by (75400-69400) = $6000

9.For what range of profit contributions for DVD players will the current solution remain optimal?

Range of profit contribution: $49-$64.

10.What happens to profit if this value drops to $50 per DVD player?

It decreases to $65160

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