1. A local pastry shop sells a whipped-cream layer cake. It costs $10 to prepare

Question

1. A local pastry shop sells a whipped-cream layer cake. It costs $10 to prepare each cake and fresh cakes sell for $20. The demand for the cakes can be approximated by a Normal distribution with mean = 10 and standard deviation = 3. Any left-over cakes can be sold the next day for $8 each.

(A) What is the optimal number of cakes to make each day?

(B) If the bakery capacity is such that only 11 cakes can be made per day, then what is the service level if 11 cakes are made each day?(That is what is the probability that demand is less than or equal to 11?

Explanation / Answer

Cost of overage (O)= cost price - salvage = 10 - 8 = 2

cost of underage (U) = selling price - cost = 20 - 10 = 10

we choose such that probability more than : U/(O+U) = 10/(10+2) = 10/12 = 0.8333

we find z value corresponding to probability = 0.8333

z = 0.97

Hence we make = mean + 0.97*standard deviation = 10 + 0.97*3 = 12.91

13 cakes to be made each day.

b)

service level = z

we have total capacity = 11

mean = 10

excess = 11 - 10 = 1

1 = z*standard deviation

z = 1/3 = 0.33

Hence service level = 0.33

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