Question

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 60 and a standard deviation of 27.

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.)

To maximize the store's expected profit ___?

c. Suppose the store manager has 98 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.)

Expected left over inventory ___?

Answer 1

Answer b

* - Dear student, Since you have not provided the table along with the question. I have used Excel to calculate the Z-value corresponding to the Critical ratio. The value calculated by Excel are more precise than the approximated values we take from the table. Hence the Final answer may vary a little bit if the assignment expected you to use the Table. If the happens then, find the Z-values corresponding to the Critical ratio and use that in the below formula to find the Optimum Quantity.
Q = μ + (σ*z)

Answer c

Dear Student,
Please ask, if you have any doubts through the comment section. Do rate the answer.