p Price 0.6 c Cost 0.2 v Salvage cost 0.11 (.99/6) * 2/3 Co Overage cost 0.09 Cu
ID: 372797 • Letter: P
Question
p Price 0.6
c Cost 0.2
v Salvage cost 0.11 (.99/6) * 2/3
Co Overage cost 0.09
Cu Underage cost 0.4
cu/(cu+co) Critical ratio 0.816326531 P value
m Mean Demand 54
s Std Dev Demand 21
Required 72.93053567 m + z*s Alternately (=norminv (P value, m, s)
A. so it should produce 73 bagels
B.
So for this the salvage value becomes new salvage value, using it:
p Price 0.6
c Cost 0.2
v Salvage cost 0.11 (.99/6) * 2/3
V' New Salvage cost 5.11
c-v' Co Overage cost -4.91
p-c Cu Underage cost 0.4
cu/(cu+co) Critical ratio -0.0886918 P value
As P becomes negative. It needs a 100% stocking to make profit.
So.
m Mean Demand 54
s Std Dev Demand 21
Required 179.9539474 m + z*s Alternately (=norminv (P value= 0.9999999, m, s)
Hence 180 is the new stock.
C.
As in Ideal scenario with the original demand, the optimal demand is 73.
So the remaining quantity is 101-73 = 28
Explanation / Answer
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 8 pm. It costs approximately S0.20 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 50.99 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 60 and standard deviation 23 If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method How many bagels should the store have at 3 pm to maximize the store's expected profit (from sales betveen 3 pm until closing)? (Hint: Assume day-old bagels are sold for $0.99/6 = $0.165 each i.e., don't worry about the fact that day-old bagels are sold in bags of six.) Use Table 13.4 and round-up rule Suppose the store manager has 101 bagels at 3 pm. How many bagels should round-up rule Round your answer to a whole number.) Suppose the manager would like to have a 0.91 in-stock probability on demand ensure that level of service? Use Table 13.4 and round-up rule b. the store manager expect to have at the end of the day? Use Table 13.4 and c. that occurs after 3 pm. How many bagels should the store have at 3 p.m. to
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