# Question: A company owns both a factory to produce its products

A company owns both a factory to produce its products and a retail outlet to sell them. A certain new product will be sold exclusively through this retail outlet. Its inventory of this product will be replenished when needed from the factory’s inventory, where an administrative and shipping cost of \$200 is incurred each time this is done. The factory will replenish its own inventory of the product when needed by setting up for a quick production run. A setup cost of \$5,000 is incurred each time this is done. The annual cost for holding each unit is \$10 when it is held at the factory and \$11 when it is held at the retail outlet. The retail outlet expects to sell 100 units of the product per month. All the assumptions of the model for a serial two-echelon system presented in Sec. 18.5 apply to the joint inventory system for the factory and retail outlet.
(a) Suppose that the factory and the retail outlet separately optimize their own inventory policies for the product. Calculate the resulting Q*2, n*, n, Q*1, and C*.
(b) Suppose that the company simultaneously optimizes the joint inventory policy for the factory and retail outlet for the product. Calculate the resulting Q*2, n*, n, Q*1, and C*.
(c) Calculate the percentage decrease in the total variable cost per unit time C* that is achieved by using the approach described in part (b) instead of the one in part (a).

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