7. Every year in early October Steven King buys pumpkins of one size from a farm
ID: 2926761 • Letter: 7
Question
7. Every year in early October Steven King buys pumpkins of one size from a farmer in Maine and then hires an artist to carve bewitching faces in them. He then tries to sell them at his produce stand in a public market in Boston.
The farmer charges Steven $2.00 per pumpkin and the artist is paid $3.00 per carved pumpkin. Steven sells a carved pumpkin for $8.00. Any pumpkins not sold by 5:00 p.m. on Halloween are donated to Steven's favorite children's hospital. Steven pays the artist $.5 per pumpkin to rush the pumpkins to the hospital for the youngsters to enjoy.
Steven estimates the demand for his pumpkins this season to be uniformly distributed within a range of 40 to 80.
a.
How many pumpkins should Steven have available for sale?
b.
Based on your answer to (a), what is the probability that Steven will be short pumpkins?
a.
How many pumpkins should Steven have available for sale?
b.
Based on your answer to (a), what is the probability that Steven will be short pumpkins?
Explanation / Answer
Single-period Inventory Model - Steven King & Pumpkin
Cost of overestimating = Co = Farmer charges + Artist Charges + Transportation charges to rush to hospital
= $2.00 + $3.00 + $0.50 = $5.50
Cost of underestimating = Cu = Selling price - Cost price = $8.00 - $5.00 = $3.00
Probability(demand <= Q*) = Cu / (Cu + Co) = 3 / 8.5 = 0.353
Since the demand follows uniform distribution with an average ranging from 40 - 80, average demand can be taken as 60.
So, the number of pumpkins recommended to be held 40 + (80-40) * (3/8.5) = 40 + 14.12 = 54.12
The probability that P(demand >= Q*) and there would be shortage of pumpkins = 1 - 0.353 = 0.647. This is really huge.
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