A fishing rod manufacturer sells its rods exclusively through Canadian Depot. Canadian Depot has to place its orders well before the peak season. On the average, each rod costs $20 to manufacture and is sold to Canadian Depot for $55. The average retail price at Canadian Depot is $100. Any unsold units at the end of the season are unlikely to have much value for Canadian Depot and will be salvaged for $20. Demand is anticipated to follow the following discrete distribution:
Probability Demand (in 1000 sqft)
.10 6
.20 7
.20 8
.35 9
.15 10

a) How many units should Canadian Depot order? What is Canadian Depot’s optimal expected profit?

b) What is the expected number of items Canadian Depot will be short (expected shortage)?

c) What is the expected number of items that will be salvaged (expected overage) at price $20 per unit?

d) What is the expected number of items Canadian Depot will sell (expected sales)?

e) Suppose that the operations manager at Canadian Depot knows the unit value of their end of season excess inventory, s, which is not $20. Based on this information Canadian Depot decides to place an order of 7000 units, what range do you think this new salvage value, s, is in?
Suppose that the anticipated demand is, actually, normally distributed with a mean of μ=7,850 and a standard deviation of s = 1,500.

f) Find the new order quantity assuming the salvage value is $20 per unit.

g) With the new demand information, find the salvage value s such that Q=7000 units is the optimal order quantity.