Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per month. Its trucking company charges Prefab $400 per shipment, independent of the quantity purchased. The manufacturer offers an all unit quantity discount with a price of $1 per square foot for orders under 20,000 square feet, $0.98 per square foot for orders between 20,000 square feet and 40,000 square feet, and $0.96 per square foot for orders larger than 40,000 square feet. Prefab incurs an annual holding cost of 20 percent. What is the optimal lot size for Prefab?

What is the annual cost of such a policy? What is the cycle inventory of plywood at Prefab? How does it compare with the cycle inventory if the manufacturer does not offer a quantity discount but sells all plywood at $0.96 per square foot?

Now consider the case in which the manufacturer offers a marginal unit quantity discount for the plywood. The first 20,000 square feet of any order are sold at $1 per square foot, the next 20,000 square feet are sold at $0.98 per square foot, and any quantity larger than 40,000 square feet is sold for $0.96 per square foot. What is the optimal lot size for Prefab given this pricing structure? How much cycle inventory of plywood will Prefab carry given the ordering policy?