The Electro-Poly Corporation is the world's leading manufacturer of slip rings. A slip ring is an electrical coupling device that allows current to pass through a spinning or rotating connection—such as a gun turret on a ship, aircraft, or tank. The company recently received a $750,000 order for various quantities of three types of slip rings. Each slip ring requires a certain amount of time to wire and harness. The following table summarizes the requirements for the three models of slip rings.

 

	Model 1	Model 2	Model 3
Number ordered	3000	2000	900
Hours of Wiring Required per Unit	2	1.5	3
Hours of Harnessing Required per Unit	1	2	1

 

 

Unfortunately, Electro-Poly does not have enough wiring and harnessing capacity to fill the order by its due date. The company has only 10,000 hours of wiring capacity and 5,000 hours of harnessing capacity available to devote to this order. However, the company can subcontract any portion of this order to one of its competitors. The unit costs of producing each model in-house (including direct labor, direct materials and other related costs) and buying the finished products from a competitor are summarized in the following table.

 

	Model 1	Model 2	Model 3
Cost to Make	$50	$83	$130
Cost to Buy	$61	$97	$145

 

 

Electro-Poly wants to determine the number of slip rings to make and the number to buy in order to fill the customer order at the least possible cost.

 

The following are the LP formulation, the optimal solution and the sensitivity report of Electro-Poly's problem.

 

  

Your Task:

You cannot use Excel to help you answer these questions. Please provide explanation to get credit.

1. How much can the unit cost of making model 1 slip rings increase before it becomes more economical to buy some of model 1 slip rings? Explain.
2. If the cost of buying model 2 slip rings decreased to $88 per unit, how would the optimal solution change (product mix, product quantities and objective function value)? Explain.
3. Assume workers in the wiring area normally make $12 per hour and get 50% more when they work overtime. Should Electro-Poly schedule these employees to work overtime to complete this job? Explain.
4. Assume workers in the harnessing area normally make $12 per hour and get 50% more when they work overtime. Should Electro-Poly schedule these employees to work overtime to complete this job? Explain.
5. Suppose a worker who performs harnessing calls in sick. Now eight fewer hours are available for harnessing hours. How would the optimal solution change (product mix, product quantities and objective function value)? Explain.
6. Suppose the client revised the order for model 1. The number ordered for model 1 now is 2,900 units. How would the optimal solution change (product mix, product quantities and objective function value)? Explain.
7. Suppose 100 units of model 3 slip rings ordered by the client require a special operation and Electro-Poly does not have the capability to do this operation. Therefore, Electro-Poly has to buy these 100 units of model 3 slip rings from its competitor for $145. What will be the impact (product mix, product quantities and objective function value)? Explain.
8. Suppose the costs of making model 1 slip rings and model 2 slip rings are increased by $2 and $5, respectively. How would the optimal solution change (product mix, product quantities, and objective function value)? Explain.

Transcribed Image Text:

M₁ = Number of model i slip rings to make in-house, i = 1, 2, 3 B₁ = Number of model i slip rings to buy from competitor, i = 1, 2, 3 MIN: Subject to: Costs Model 1 demand Model 2 demand Model 3 demand Hours of wiring Hours of harnessing 50M₁ + 83M₂ + 130M3 + 61B₁ + 97B2 + 145B3 M₁ + 3,000 M₂ + 2,000 M3 + 900 2M₁ + 1M₁ + M₁ 3000 50 1 2 1 1 M₂ 550 900 83 130 1.5 52 2 B1 B₂ B3 1 3 1 1.5M₂ + 3M3 M 2M₂ + 1M3 < M₁, M₂, M3, B₁, B₂, B3 ≥ = 1 = M3 B₁ B₂ B3 0 1450 0 61 97 145 453300 1 3000 2000 900 9525 10000 5000 5000 1 = 10,000 5,000 0 3000 2000 900 M₁ = Number of model i slip rings to make in-house, i = 1, 2, 3 B₁ = Number of model i slip rings to buy from competitor, i = 1, 2, 3 MIN: Subject to: Costs Model 1 demand Model 2 demand Model 3 demand Hours of wiring Hours of harnessing 50M₁ + 83M₂ + 130M3 + 61B₁ + 97B2 + 145B3 M₁ + 3,000 M₂ + 2,000 M3 + 900 2M₁ + 1M₁ + M₁ 3000 50 1 2 1 1 M₂ 550 900 83 130 1.5 52 2 B1 B₂ B3 1 3 1 1.5M₂ + 3M3 M 2M₂ + 1M3 < M₁, M₂, M3, B₁, B₂, B3 ≥ = 1 = M3 B₁ B₂ B3 0 1450 0 61 97 145 453300 1 3000 2000 900 9525 10000 5000 5000 1 = 10,000 5,000 0 3000 2000 900

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1 much can the unit cost of making model 1 slip rings increase before it becomes more economical to buy some of model 1 slip rings The shadow price for the Model 1 demand constraint is 57 This represe... View the full answer