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Question

Problem 9: Consider the following demand scenario:  Consider the following demand scenario:

 Quantity Probability 2000 3% 2100 8% 2200 15% 2300 30% 2400 17% 2500 12% 2600 10% 2700 5%

Suppose the manufacturer produces at a cost of \$20/unit. The distributor sells to end customers for \$50/unit during season and unsold units are sold for \$10/unit after season.

b) Suppose the manufacturer is make-to-order (i.e., the distributor must order before it receives demand from end customers).

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(i) Suppose the manufacturer sells to the distributor at \$40/unit, how much should the distributor order? What is the expected profit for the manufacturer? What is the expected profit for distributor?

(ii) Find an option contract such that both the manufacturer and distributor enjoy a higher expected profit than (b)(i). What is the expected profit for the manufacturer and the distributor?

I don’t necessarliy need the answer- but to understand how to get it. Since the MFG produces what is ordered their cost and profit is what ever the quanity is. How do I go about figuring out much the distributer should order? Do I do a demand equation? I am totally lost