Question

CPG Bagels starts the day with a large production run of bagels. Throughout the morning, additional bagels are produced as needed. The last bake is completed at 3 p.m. and the store closes at 8 p.m. It costs approximately $0.20 in materials and labor to make a bagel. The price of a fresh bagel is $0.60. Bagels not sold by the end of the day are sold the next day as “day old” bagels in bags of six, for $0.99 a bag. About two-thirds of the day-old bagels are sold; the remainder are just thrown away. There are many bagel flavors, but for simplicity, concentrate just on the plain bagels. The store manager predicts that demand for plain bagels from 3 p.m. until closing is normally distributed with a mean of 54 and a standard deviation of 21.

a. How many bagels should the store have at 3 p.m. to maximize the store’s expected profit (from sales between 3 p.m. until closing)? (Hint: Assume day-old bagels are sold for $0.99/6 = $0.165 each; that is, don’t worry about the fact that day-old bagels are sold in bags of six.) (Round your answer to the nearest whole number.)

To maximize the store's expected profit ___?

b. Suppose that the store manager is concerned that stockouts might cause a loss of future business. To explore this idea, the store manager feels that it is appropriate to assign a stockout cost of $5 per bagel that is demanded but not filled. (Customers frequently purchase more than one bagel at a time. This cost is per bagel demanded that is not satisfied rather than per customer that does not receive a complete order.) Given the additional stockout cost, how many bagels should the store have at 3 p.m. to maximize the store’s expected profit? (Round your answer to the nearest whole number.)

To maximize the store's expected profit ___ ?

c. Suppose the store manager has 121 bagels at 3 p.m. How many bagels should the store manager expect to have at the end of the day? (Round your answer to the nearest whole number.)

Expected Left Over Inventory ___?

Answer 1

c)

121 -54 / 21 = 3.19

L(3.19) = 0.0002

Expected lost sales = SD x L(z) = 21 * 0.0002 = 0.0042

Expected left over inventory = 121 - 54 + 00042 = 67.0042 = 67

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