Each year the Smalltown branch of a furniture store sells 20,000 dining room tables. The local store orders tables from the company warehouse providing stock for many local branches and the cost of doing this is $15 per table plus a fixed cost of $100 per order. Assume that the lead time is zero. The store’s manager believes that the demand for tables can be backlogged and that the cost of being short one table for one year is $25. The annual holding cost for inventory is 30¢ per dollar value of inventory.
(a) What is the optimal order quantity?
(b) If the store manager orders the order quantity found in part (a), what is the maximum shortage that will occur?
(c) At most, how many tables can the Smalltown furniture store have in stock if the optimal ordering policy is followed?
(d) What is the average cost per year under the optimal policy?