Cynthia Knott\'s oyster bar buys fresh Louisiana oysters for $4 per pound and se
ID: 463822 • Letter: C
Question
Cynthia Knott's oyster bar buys fresh Louisiana oysters for $4 per pound and sells them for $8 per pound. Any oysters not sold that day are sold to her cousin, who has a nearby grocery store, for $2 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 120 pounds and a standard deviation of 16 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
Here we have,
Cost of under-stocking (Cu) = $8 - $ 4 = $4
The profit that Cynthia Knott’s lose not being able to sell the oysters
Cost of over-stocking (Co) is: $4 - $ 2 = $2
The amount that Cynthia Knott’s lose because she have to sell at a discount to her cousin
The optimal service level (SL) or target service level = Cu/(Cu +Co)
= 4 /(4+2) =0.6667 or 66.67%
Optimal order quantity Q = D+ z
Where D is the average daily demand = 120 pounds
And is the standard deviation of demand = 16 pounds
Z at 66.67 % service level = 0.4308
Optimal order quantity Q = D+ z
Q = 120 + 0.4308 * 16 = 120+ 6.89 = 126.89 pounds
Cynthia Knott’s should order 126.9 pounds of oysters each day
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.