Consider the problem of Inventory Management for a store that sells frozen foods. The store expects to sell 50,000 pounds of frozen foods in a year and they need to decide what size refrigeration unit to purchase. The cost of the refrigeration unit is 8000+0.4s dollars, where s is the maximum number of pounds of frozen food that the refrigeration unit will hold. It costs the same amount to run the refrigeration unit no matter how much frozen food is in it, but that cost is 6s dollars per year. We assume that the store will arrange to have new shipments of frozen food arrive just as their existing inventory runs out (this is called Just in Time inventory control). This means each shipment of new inventory should contain s pounds of frozen food. Let N be the number of deliveries required in a given year. The delivery costs are 300+0.06s dollars per delivery. Finally, it is likely that the refrigeration unit has a useful life of only five years, so let's assume that the cost of the refrigeration unit is spread out evenly over a five-year period.
a) Give a formula for the annual inventory control costs, C, as a function of the maximum storage size, s (This would only be valid for the first five years.)
b) To the nearest pound, what size refrigeration unit should the store purchase?
Suppose now that the store owner is worried about power outages spoiling all his inventory. He decides to insure his inventory against loss. His insurance agent agrees to insure the total value of the inventory at any given time for 50 cents per pound per year, calculated on the maximum number of pounds of inventory that are ever in the refrigeration unit.
c) Taking into account the insurance costs, to the nearest pound, what size refrigeration unit should the store purchase?