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.

(a) 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 a 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?

(b) Now consider the case where the manufacturer now 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?