### How many units of the product should the retailer order

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##### Reference no: EM13500616

Supply Chain Coordination

A supplier manufactures a product at cost m = \$40 and sells it to a retailer at wholesale price c = \$100. The retailer sells this product to consumers at retail price p = \$200. The replenishment lead time for this product is long relative to the selling season, so the retailer only has one opportunity to stock the product. Demand for the product is normally distributed with a mean of 1000 units and a standard deviation of 400 units. Units unsold at the end of the season are salvaged at price v = \$15.

a. How many units of the product should the retailer order to maximize  its expected profit? What is the associated retailer's expected  profit and the supplier's expected profit?

Number of Units to Order ____________

Retailer's Expected Profit ____________

Supplier's Expected Profit ____________

b. how many units of the product should the retailer order to maximize  total supply chain expected profit? What is the associated  retailer's expected profit and the supplier's expected profit?

Number of Units to Order __________

Retailer's Expected Profit ______________

Supplier's Expected Profit _____________

c. To motivate the retailer to buy more product, the supplier offers  the following deal: the wholesale price is reduced to c =  \$80, but the retailer must pay the supplier an additional \$40 for every  unit that it sells. The supplier is also willing to buy back units  that the retailer is unable to sell at buyback price b. These  units are then salvaged by the supplier. What value of b should the supplier offer to maximize total supply chain expected  profit? What is the associated retailer's expected profit and the  supplier's expected profit?

Retailer's Expected Profit _______________

Supplier's Expected Profit _

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