1-A soap manufacturer has dedicated a plant for one major retail chain. Sales at the retail chain average about 10,000 jugs of soap a month and production at the plant keeps pace with this average demand. Each jug of soap costs the manufacturer 5 and is sold to the retailer at a wholesale price of 10. Both the manufacturer and the retailer use an annual holding cost of 25 percent. For each order placed, the retailer incurs an ordering cost of 100. The 

manufacturer incurs the cost of transportation and loading that totals 1,600 per order shipped.

 

1. 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 
2. ordering and holding costs for the manufacturer as a result of this policy? What is the total inventory cost across both parties as a result of this policy?
 
3. What lot size minimizes the inventory costs (ordering, delivery, and holding) across both the manufacturer and the retailer? How much reduction in cost relative to (a) results from this policy?
4. Design an all unit quantity discount that results in the retailer ordering the quantity in (b).

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