Question

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A small grocery store sells fresh produce, which it obtains from a local farmer. During the strawberry season, demand for fresh strawberries can be reasonably approximated using a Normal distribution with a mean of 40 quarts per day and a standard deviation of 6 quarts per day. Excess costs run $0.39 per quart. The grocer orders 49 quarts per day. What is the implied cost of shortage per quart? Answer: Check

Answer 1

Mean Demand = $\mu$ = 40 quarts

Std. Deviation = $\sigma$ = 6 quarts

Order Quantity = Q =49 quarts

We find Z value as:

Z = $\frac{Q-\mu }{\sigma }$ = $\frac{49-40 }{6 }$ = 1.5

For Z = 1.5, Service level = 93.31%

We know,

Service level = $\frac{Cs }{Cs+Ce }$ where Ce is excess cost and Cs is shortage cost

Ce = $0.39 per quart

0.9332 = $\frac{Cs }{Cs+0.39 }$

0.9332 Cs + 0.364 = Cs

Cs = $5.44

Answer: 5.44

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