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. Prefab incurs a holding cost of 20 percent. Prefab has decided to offer a marginal unit 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.   Question:   What is the optimal lot size for given this pricing structure?   How much cycle inventory of plywood will Prefab carry given the ordering policy?   How does this lot size compare with the cycle inventory if Prefab does not offer a quantity discount but sells all plywood at $0.96 per square foot?

Practical Management Science
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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. Prefab incurs a holding cost of 20 percent. Prefab has decided to offer a marginal unit 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.

 

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What is the optimal lot size for given this pricing structure?

 

How much cycle inventory of plywood will Prefab carry given the ordering policy?

 

How does this lot size compare with the cycle inventory if Prefab does not offer a quantity discount but sells all plywood at $0.96 per square foot?

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