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 pm, and the store closes at 8pm. It cost approximately $015 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 previous day are sold the next day as "day ld" 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 pm until closing is normally distributed with mean 58 and standard deviation 25.

a) how many bagels should the store have at 3pm to maximize the store's expected profit (from sales between 3pm until closing)? (hint: assume day-old bagels are sold for $0.99/6= $0.165 each, ie don't worry about the fact that day old bagels are sold in bags of six.) use the round up rule.

b) suppose the store manager has 102 bagels at 3pm. how many bagels should the store manager expect to have at the end of the day? use the round up rule.

c) suppose the manager would like to have a 0.95 in stock probablity on demand that occurs after 3pm. how many bagels should the store have at 3pm to ensure that level of service? use the round up rule.