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 39,999 square feet, and $0.96 per square foot for orders greater than or equal to 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?

All Unit Discount

Fixed cost per order		per order
Monthly demand		sq feet
Holding percentage		%

Pricing

min Qty	max Qty	Price per sq ft
0	19,000
20,000	40,000
40,000

Range i	Q	Adjust to q	total cost
1
2
3

Without Quantity Discount

Price per sq ft	Q	Total cost