roblem 12.52 - Question Help | * Henrique Correa\'s bakery prepares all its cake
ID: 361306 • Letter: R
Question
roblem 12.52 - Question Help | * 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 $16 price. The cost of baking a cake is $10, and demand is estimated to be normally distributed, with a mean of 25 and a standard deviation of 7. 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
This problem will be solved using Newsvendor model
Given are following data :
Average demand = m = 25
Standard deviation of demand = Sd = 7
Sale price = P = $16/ unit
Cost of cake = C = $10 / unit
Salvage price = S = 50% of $16 = $8 / unit
Thus ,
Cost of underordering = Cu = P – C = $16 - $10 = $6 / unit
Cost of overordering = Co = C – S = $ 10 - $ 8 = $ 2/ unit
Therefore,
Critical ratio = Cu/ ( Cu + Co) = 6/ ( 6 + 2) = 6/8 = 0.75
Critical ratio is the probability of optimum stocking level . Corresponding Z value for such optimum stocking level = NORMSINV ( 0.75 ) = 0.6745
Therefore , Optimum stocking level for the Bakery
= m + Z x Sd
= 25 + 0.6745x 7
= 25 + 4.72
= 29.72 ( 30 rounding to next higher whole number )
OPTIMUM STOCKING LEVEL FOR THE BAKERY = 30
OPTIMUM STOCKING LEVEL FOR THE BAKERY = 30
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