A small grocery store sells fresh produce, which it obtains from a local farmer.

Question

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 42 quarts per day and a standard deviation of 4 quarts per day. Excess costs run .30 cents per quart. The grocer orders 45 quarts per day.

What is the implied cost of shortage per quart? (Round your z value to 2 decimal places, your service level probability to 4 decimal places and your final answer to 2 decimal places. Omit the "$" sign in your response.)

What is the implied cost of shortage per quart? (Round your z value to 2 decimal places, your service level probability to 4 decimal places and your final answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

order = 45

mean = 42

standard deviation = 4

z is the standard normal distribution score

order = mean + z*standard deviation

45 = 42 + z*4

z = 0.75

using standard normal distribution tables, probability at z = 0.75:

probability = 0.7734

Cost of excess or cost of overage is given (Co) = 0.3

cost of shortage of underage (Cu)

Cu/ (Cu + Co) = 0.7734

Cu/(Cu + 0.3) = 0.7734

Cu = 0.7734Cu + 0.3*0.7734

0.2266Cu = 0.23202

Cu = 1.024

implied cost of shortage = 1.024

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