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 3:00 pm and the store closes at 8:00 pm. 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 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 remainders are just thrown away. There are many bagel flavors, but for simplicity, concentrate on plain bagels. The store manager predicts that demand for plain bagels from 3:00 pm until closing are normally distributed with mean of 54 and standard deviation of 21.
a. How many bagels should the store have at 3:00 pm to maximize the store's expected profit from sales between 3:00 pm until closing? Assume day-old bagels are sold for $0.99/6=$0.165 each, i.e., do not worry about the fact that day old bagels are sold in bags of six.
b. Suppose the manager would like to ensure at least 99% service level on demand that occurs after 3:00 pm. How many bagels should the store have at 3:00 pm?
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
d. Stock-out cost of $5.00 per bagel that is demanded but not filled. Given this additional cost, how many bagels should the store have at 3:00 pm to maximize the expected profit?
Additional Requirement
The question lies to Supply Chain Management and it is about CPG Bagels which produces and sells bagels. Every day there is a significant amount of bagels are thrown away as old stock. The company wants to reduce this wastage. For this company wants to study how many average bagels are sold and thus make bagels accordingly.