mathxl.com Henrique Correa\'s bakery prepares al its cakes between 4 A.M.and 6 A
ID: 2925328 • Letter: M
Question
mathxl.com Henrique Correa's bakery prepares al 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 $8 price. The cost of baking a cake is S5, and demand is estimated to be normally distributed with a mean of 30 and a standard deviation of 3. What is the optimal stocking level? Refer to the standard normal table for z-values. The optimal stocking level for the bakery is cakes (round your response to the nearest whole number).Explanation / Answer
Solution:
Cost of shortage, Cu = profit per unit = selling price - cost price = $8 - $5 = $3
Cost of overage Co = Cost - salvage value = $5 - $8*50% = $5 - $4 = $1
Critical ratio or optimal service level = Cu / (Cu + Co) = 3 / (3 + 1) = 0.75
Z-value corresponding to 0.75 service level = NORMSINV(0.75) = 0.6745 (or refer to Standard normal table for z-value)
Therefore optimal stocking level for the bakery = + Z* = 30 + 0.6745*3 = 32 cakes
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