Cynthia Knott\'s oyster bar buys fresh Louisiana oysters for $33 per pound and s
ID: 463693 • Letter: C
Question
Cynthia Knott's oyster bar buys fresh Louisiana oysters for
$33
per pound and sells them for
$99
per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for
$22
per pound. Cynthia believes that demand follows the normal distribution, with a mean of
100
pounds and a standard deviation of
10
pounds. How many pounds should she order each day? Refer to the standard normal table for z-values.Cynthia should order ??? pounds of oysters each day (round your response to one decimal place).
Explanation / Answer
Using Single period inventory model, we can calcualte the daily ordering quantity as shown below:
P = Probability that the unit will sold is calculated using following formual;
Cost of overestimation, Co = $ 21/pound
Cost of Underestimation, Cu = $ 66/pound
P <= Cu/(Co+Cu) = 66/(21+66) = 0.7583
Mean,m = 100 pounds
Std. Dev, s = 10 pounds
Z value (P=0.7583) = 0.700
Every day order quantity = m + Z x s = 100+0.700 x 10 =107 pounds
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