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 65 and a standard deviation of 32 . 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.) 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.) c. Suppose the store manager has 107 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.)