A pharmacist wants to establish an optimal inventory policy for a new antibiotic that requires refrigeration in storage. The pharmacist expects to sell 800 packages of this antibiotic at a steady rate during the next year. She plans to place several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is $16, and carrying costs, based on the average number of packages in inventory, amount to $4 per year for one package.

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