CPG Bagels:-

CPG Bagels sta11s 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 mean of 54 and standard deviation of 21.

a. How many bagels should the store have at 3 p.m. to maximize the stores expected profit (from sales between 3 p.m. until closing)?

b. Suppose the manager would like to ensure at least a 99 percent fill rate on demand that occurs after 3 p.m. How many bagels should the store have at 3 p.m. to ensure that fill rate?

c. Suppose that the store manager is concerned that stock outs 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 stores expected profit?

d. Suppose the store manager has 101 bagels at 3 p.m. How many bagels should the store manager expect to have at the end of the day?