Problem 13-37 A small grocery store sells fresh produce, which it obtains from a
ID: 425101 • Letter: P
Question
Problem 13-37 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 8 quarts per day. Excess costs run.45 cents per quart. The grocer orders 47 quarts per day. Use Table. 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 "$" sign in your response.) Shortage cost per quart$Explanation / Answer
The problem will be solved using principle of Newsvendor model
As per above ,
Order quantity per day = Mean demand per day + Critical ratio x standard deviation of demand per day
Let Z value = Z1
Therefore ,
47 = 40 + 8.Z1
Or, 8.C = 7
Or, Z1 = 7/8 = 0.875
Corresponding probability for z = 0.875 as derived from standard normal distribution table = 0.8092
This probability of 0.8092 is termed as “Critical Ratio”
Let implied cost of shortage per quart = $ Cu
Excess cost per quart = Co = $0.45
Since , Critical ratio = Cu/ ( Cu + Co )
Therefore ,
Cu / ( Cu + 0.45 ) = 0.8092
Or, ( Cu + 0.45) /Cu = 1/0.8092
Or, 1 + 0.45/Cu = 1.2357
Or, 0.45/Cu = 0.2357
Cu = 0.45/0.2357
Or, Cu = 1.909 ( 1.91 rounded to nearest whole number )
SHORTAGE COST PER QUART = $1.91
SHORTAGE COST PER QUART = $1.91