Question

You are in charge of ordering programs for the Toronto Maple Leaf games. Because they are specific to an opponent, any leftover programs you have are recycled. Demand for programs is uniformly distributed from 3500 to 6500. The programs cost you $1.5 to print and you sell them for $8.0. How many programs should you order each game to maximize expected profits over

Question 31 (2 points)

Consider your answer in Question 30. If you could get $0.50 for unused Programs from a memorabilia company, what would happen to your optimal order?

Question 31 options:

	stay the same.
	go up.
	go down.
	it depends on the distribution of demand.

Answer 1

1. B. GO UP

FOR UNIFORM DISTRIBUTION:

MEAN = (B + A) / 2 = (6500 + 3500) / 2) = 5000
STDEV = (B - A) / SQRT(12) = (6500 - 3500) / SQRT(12) = 866.03

COST PRICE = 1.5
SALES PRICE = 8
SALVAGE VALUE = 0

COST OF SHORTAGE(CS) = SALES PRICE - COST PRICE = 8 - 1.5 = 6.5
COST OF OVERAGE(CO) = COST PRICE - SALVAGE VALUE = 1.5 - 0 = 1.5

SERVICE LEVEL = CS / (CS + CO) = 6.5 / (6.5 + 1.5) = 0.8125
THE Z VALUE THAT CORRESPONDS TO A SERVICE LEVEL OF 0.8125 IS = 0.887

MEAN DEMAND = 5000
STANDARD DEVIATION = 866.03

OPTIMAL STOCKING LEVEL = MEAN DEMAND + (Z * STANDARD DEVIATION)

= 5000 + (0.887 * 866.03) = 5768

WITH 0.5 AS SALVAGE COST

COST PRICE = 1.5
SALES PRICE = 8
SALVAGE VALUE = 0.5

COST OF SHORTAGE(CS) = SALES PRICE - COST PRICE = 8 - 1.5 = 6.5
COST OF OVERAGE(CO) = COST PRICE - SALVAGE VALUE = 1.5 - 0.5 = 1

SERVICE LEVEL = CS / (CS + CO) = 6.5 / (6.5 + 1) = 0.8667
THE Z VALUE THAT CORRESPONDS TO A SERVICE LEVEL OF 0.8667 IS = 1.111

MEAN DEMAND = 5000
STANDARD DEVIATION = 866.03

OPTIMAL STOCKING LEVEL = MEAN DEMAND + (Z * STANDARD DEVIATION)

= 5000 + (1.111 * 866.03) = 5962

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