River City Cement Co. maintains an inventory of lime that is purchased from a local supplier. River City uses an average of 200,000 pounds of lime annually in its manufacturing operations (assume 50 operating weeks per year). The lime is purchased from the supplier at a cost of $0.10 per pound. The inventory holding cost is 30 percent of the average value of the inventory, and the cost of placing an order for replenishment is estimated to be $12 per order.
a. Assume that River City orders 10,000 pounds of lime every time it places an order for replenishment. What is the average annual cost of maintaining the inventory?
b. Determine the EOQ. If the forecast of annual demand is 10 percent less than actual, how much "extra" is River City paying annually because of an inaccurate forecast of demand (note that this means actual demand for lime averages 220,000 pounds)?
c. Assume that the supplier offers River City a 10 percent "all units" discount if the order quantity is 13,000 pounds or more. Also, assume that annual demand for lime averages 200,000 pounds. What is the best order quantity?