1. Consider the following demand scenario: Quantity Probability 2,000 2,100 3% 8% 2,200 15% 2,300 2,400 30% 17% 2,500 12% 2,600 10% 2,700 5% Suppose the manufacturer produces at a cost of $20/unit and sells to the distributor at $40/unit. The distributor sells to end customers for $50/unit during season; unsold units are sold for $10/unit after season. 1. Assume the manufacturer will buy any unsold items at price $32/unit. What is the optimal order quantity? 2. What is the expected number of unsold items? 3. What is the profit for the distributor?

Practical Management Science
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Author:WINSTON, Wayne L.
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1. Consider the following demand scenario:
Quantity
Probability
2,000
3%
2,100
8%
2,200
2,300
15%
30%
2,400
17%
2,500
12%
2,600
10%
2,700
5%
Suppose the manufacturer produces at a cost of $20/unit and sells to the distributor at $40/unit. The
distributor sells to end customers for $50/unit during season; unsold units are sold for $10/unit after
season.
1. Assume the manufacturer will buy any unsold items at price $32/unit. What is the optimal order
quantity?
2. What is the expected number of unsold items?
3. What is the profit for the distributor?
4. What is the profit for the supplier?
Transcribed Image Text:1. Consider the following demand scenario: Quantity Probability 2,000 3% 2,100 8% 2,200 2,300 15% 30% 2,400 17% 2,500 12% 2,600 10% 2,700 5% Suppose the manufacturer produces at a cost of $20/unit and sells to the distributor at $40/unit. The distributor sells to end customers for $50/unit during season; unsold units are sold for $10/unit after season. 1. Assume the manufacturer will buy any unsold items at price $32/unit. What is the optimal order quantity? 2. What is the expected number of unsold items? 3. What is the profit for the distributor? 4. What is the profit for the supplier?
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