QUESTION 28 (10 points) Single Period Inventory Model As usual, a pharmacy chain
ID: 3174080 • Letter: Q
Question
QUESTION 28 (10 points) SinglePeriod Inventory Model
As usual, a pharmacy chain plans to sell highquality Easter eggs this year. These eggs are typically stocked at the beginning of March and need to be sold on or before Easter for full value. After Easter, the remaining eggs would be marked down to get sold. For each egg, the item cost is $2.25, the full selling price is $4.99, and the marked down price is $0.98.
You would need to show equations, steps, and the final results with units for full credits. Answers are in millions using 5 decimals, e.g. 1.76384 million eggs. For simplicity, all taxes and other costs are not considered.
(a)[5] Given that the pharmacy's historical demand is uniformly distributed from 1.1 million to 1.4 million eggs, determine how many eggs the pharmacy should carry this year.
(b)[5] Given that the pharmacy's historical demand is normally distributed with mean of 1.25 million eggs and standard deviation of 0.15 million eggs, determine how many eggs the pharmacy should carry this year.
Hint: Use the following table to find the zvalue.
*
0.54663
0.61496
0.68329
0.75162
0.81995
z = NORM.S.INV(*)
0.11716
0.29228
0.47692
0.67960
0.91518
*
0.54663
0.61496
0.68329
0.75162
0.81995
z = NORM.S.INV(*)
0.11716
0.29228
0.47692
0.67960
0.91518
Explanation / Answer
a) qopt = F-1 (p - c / p)
= F-1 (4.99 - 2.25 / 4.99)
= F-1(0.549) = Dmin + (Dmax - Dmin)*0.549
= 1.1 + (1.4-1.1)*0.549
= 1.1 + 0.1647
= 1.2647 million
b) qopt = µ + Z-1(0.549)
= 1.25 + 0.15*0.11716
= 1.2675 million
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