. 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. andthe 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 previous 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. and 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.) b. 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? c. Suppose the manager would like to have a .95 in-stock probability on demand that occurs after 3 p.m. How many bagels should the store have at 3 p.m. to ensure that level of service?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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. 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. andthe 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 previous 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. and 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.)
b. 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?
c. Suppose the manager would like to have a .95 in-stock probability on demand that
occurs after 3 p.m. How many bagels should the store have at 3 p.m. to ensure that
level of service?

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