Henrique Correa's bakery prepares all its cakes between 4 A.M.and 6 A.M.so they will be fresh when customers arrive. Day-old cakes are virtually always sold, but at a 50% discount off the regular $10 price. The cost of baking a cake is $7, and demand is estimated to be normally distributed, with a mean of 30 and a standard deviation of 6. What is the optimal stocking level? Refer to the standard normal table LOADING... for z-values.
The optimal stocking level for the bakery is cakes (round your response to the nearest whole number).
Solution:
Overage cost (Co) i.e. cost of overbuying is calculated as,
Co = Cost price - Salvage value
Salvage value = 50% of $10 = $5
Co = $7 - $5
Co = $2
Underage cost (Cu) i.e. cost of underbuying is calculated as,
Cu = Selling price - Cost price
Cu = $10 - $7
Cu = $3
Service level = Cu / (Cu + Co)
Service level = $3 / ($3 + $2)
Service level = 0.6
Using the standard normal table, value of Z can be computed. For service level = 0.6,
Z-value = 0.253
Optimal stocking level (Q):
Q = Average Demand + (Z-value x Standard deviation)
Q = 30 + (0.253 x 6)
Q = 31.52 or 32 (Rounding off to the nearest whole number)
The optimal stocking level for the bakery is 32 cakes.
Henrique Correa's bakery prepares all its cakes between 4 A.M.and 6 A.M.so they will be fresh...
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