Amy’s Ice Cream sells 180 quarts of vanilla ice cream each month. The store currently restocks its inventory at the beginning of each month. The wholesale price (value) of ice cream is $3 per quart. Assume that demand oc- curs at a constant rate and that the annual cost of holding inventory is 25% of the value of the average inventory level. Last year’s annual total cost was $7,627.50, which is comprised of three separate cost components: (1) a fixed ordering cost K for each order placed, (2) the annual cost for holding inventory, and (3) a variable cost of $3 for each quart of ice cream ordered.
(a) Compute y/2, the average inventory level.
(b) Compute the annual holding cost.
(c) Use last year’s annual total cost along with your answer to part (b) to compute K, the fixed ordering cost for each order placed.
(Hint: Be sure to use the amount of yearly demand for your value of D.)
(d) Currently, the store uses an order quantity of y = 180 quarts. Use your values of K, D (yearly), and h (what is h?) to compute the optimal order quantity y∗, and the optimal time t∗0 between orders.
(e) Use your answer to part (d) to compute the annual total cost if the optimal order quantity y∗ is used.
(f) How much will Amy’s Ice Cream save per year if it uses the optimal order quantity?