The Supermarket Store is about to place an order for Halloween candy. One best- selling brand of candy can be purchased at $ 2.40 per box and usually is sold for $ 4.25 per box before and up to Halloween. After Halloween, all the remaining candy can be sold for $ 1.00 per box. Demand for the candy at the regular price is a random variable with the following discrete probability distribution:
|
Demand (boxes)
|
Probability
|
|
8
|
0.25
|
|
9
|
0.15
|
|
10
|
0.20
|
|
11
|
0.25
|
|
12
|
0.15
|
You are required to:
a. Complete the following table to determine the optimal order quantity (Q*).
Each entry in the table represents the profit made by the store for a given combination of demand and stocking quantity.
|
Demand in
boxes
|
Probability
|
Q=8
|
Q=9
|
Q=10
|
Q=11
|
Q=12
|
|
8
|
0.25
|
|
|
|
|
|
|
9
|
0.15
|
|
|
|
|
|
|
10
|
0.20
|
|
|
|
|
|
|
11
|
0.25
|
|
|
|
|
|
|
12
|
0.15
|
|
|
|
|
|
|
Expected profit
|
|
|
|
|
|
b. Determine the optimal order quantity using the critical ratio. Does this order quantity correspond to the answer in part a?