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Consider the game that we explained in class. Assume that retailer can sell its product for $150 in the market and its demand follows a normal distribution with mean of 500 and standard deviation of 200. Retailer procures its product from a supplier for w per unit but to sell each unit it incurs a cost of $5 in terms of employment costs and also advertisement costs.

a. If supplier price is $60, what is retailer’s optimal order quantity? What is retailer’s expected profit?

b. Now assume that supplier incurs a cost of $20 to produce each unit. What is the optimal wholesale price, w which maximizes supplier’s profit?

c. What is the whole supply chain maximum expected profit? (add both firms’ profits and use Crystal Ball in Excel to find maximum expected profit, notice that w does not affect total supply chain profit)

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