Problem 13-14
Without Discount With Discount
Inputs Inputs
Expected demand 20,000 Expected demand 20,000
Standard deviation of demand 8,000 Standard deviation of demand 8,000
Unit cost, c$30 Unit cost, c$28
Sales price, p$95 Sales price, p$95
Salvage value, s$0 Salvage value, s$0
Cost of understocking, Cu$65 Cost of understocking, Cu$67
Cost of overstocking, Co$30 Cost of overstocking, Co$28
Outputs Outputs
Optimal cycle service level 0.6842 Optimal cycle service level 0.7052632
Optimal order quantity 23,836 Optimal order quantity 24,317
Order quantity 25,000
Expected profits $1,029,731 Expected profits $1,076,941
Expected overstock 5,470 Expected overstock 6,295
A designer is planning orders for its annual limited-edition ornament. Demand has been forecast to be normally distributed, with a mean of
20,000 and a standard deviation of 8,000. Each ornament costs $30 and is sold for $95. All unsold ornaments are destroyed at the end of
the season, to ensure the value of the limited edition.
a. How many ornaments should the designer order? What is the expected profit?
b. The manufacturer has offered to discount the price to $28 per ornament if at least 25,000 are ordered. How should the designer
respond?