A furniture store expects to sell 640 sofas at a steady rate next year. The manager of the store plans to order these sofas from the manufacturer by placing several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is $160, and carrying costs, based on the average number of sofas in inventory, amount to $32 per year for one sofa.

(a) Let x be the order quantity and r the number of orders placed during the year. Find the inventory cost in terms of x and r.

(b) Find the constraint function.

(c) Determine the economic order quantity that minimizes the inventory cost, and then find the minimum inventory cost.