Question

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).

Answer 1

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.