Crunchy, a cereal manufacturer, has dedicated a plant for one major retail chain. Sales at the retail chain average about 20,000 boxes a month and production at the plant keeps pace with this average demand. Each box of cereal costs Crunchy $3 and is sold to the retailer at a wholesale price of $5. Both Crunchy and the retailer use an annual holding cost of 20 percent. For each order placed, the retailer incurs an ordering cost of $200. Crunchy incurs the cost of transportation and loading that totals $1,000 per order shipped.

a. Given that it is trying to minimize its ordering and holding costs, what lot size will the retailer ask for in each order? What are the annual ordering and holding costs for the retailer as a result of this policy? What are the annual ordering and holding costs for Crunchy as a result of this policy? What is the total inventory cost across both parties as a result of this policy?

b. What lot size minimizes the inventory costs (ordering, delivery, and holding) across both Crunchy and the retailer? How much reduction in cost relative to

(a) results from this policy?

c. Design an all unit quantity discount that results in the retailer ordering the quantity in (b).

d. How much of the $1,000 delivery cost should Crunchy pass along to the retailer for each lot to get the retailer to order the quantity in

(b)?