CPG Bagels starts the day with a large production run of bagels. Throughout the
ID: 372532 • Letter: C
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 3PM, and the store closes at 8PM. 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 ate 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 bagels flavors, but for simplicity, concentrate just on te plain bagels. The store manager predicts the demand for plain bagels from 3pm until closing is normally distributed with mean 60 and standard deviation 23.
use Excel
a. How many bagels should the store have at3pm 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 Table 13.4 and round – up rule.
Co = C-SV = $0.2 - $0.165x2/3 = $0.09 Cu = P-C = $0.6 - $0.2 = $0.4 F(Q*)=P*= Cu/ (Cu+Co) = 0.4/ 0.4+0.09 = 0.81632
Q* = + NORM.S.INV(P*) x = 60+ NORM.S.INV(0.81632)x23 = 60+ 0.90143 x 23 = 80.73288 =81
b. Suppose the store manager has 101 bagels at 3pm. How many bagels should the store manager expect to have at the end of the day? round-up rule. c. Suppose the manager would like to have a 0.91 in-stock probability on demand that occurs after 3 pm. How many bagels should the store have at 3pm. To ensure that level of service? Use table 13.4 and round –up rule
Explanation / Answer
Co = C-SV = $0.2 - $0.165x2/3 = $0.09 Cu = P-C = $0.6 - $0.2 = $0.4 F(Q*)=P*= Cu/ (Cu+Co) = 0.4/ 0.4+0.09 = 0.81632
Q* = + NORM.S.INV(P*) x = 60+ NORM.S.INV (0.81632) x23 = 60+ 0.90143 x 23 = 80.73288 =81
Expected lost sales= L(z )x
Z= 0.81632
L(z )= 0.120*23 = 2.76
Expected sales = - Expected lost sales = 60-3 = 57
Expected Profit = 57*0.4= 22.8
Expected sales = - Expected lost sales = 60-3 = 57
Total Bagel at 3PM = 101
Left at the end of business hours = 101 – 57 = 44
in-stock probability = 0.91
= 60 , = 23
Q = Norminv (.91,60,23)= 90.83737