You are hired by Southwest Glass Manufacturing (SGM) to optimize their ordering decisions of one of their important raw inputs Imported Soda Ash. SGM imports natural Soda Ash from Turkey in special containers and uses a dedicated silo facility in the Port of Los Angeles, CA. SGM production facilities in Salton City, CA have continuous production (24 hours/day, 7 days/week) utilized steadily at 90% capacity, requiring 10,000 metric tons of Soda Ash each year. A metric ton of Soda Ash costs $300. The order cost is $10,000. The order lead time is 6 months. The annual holding cost of inventory is 15% of the item cost.

1. (4 pts.) Determine the optimal order quantity and the optimal total of expected annual inventory holding and setup costs.
2. (6 pts.) Suppose that the supplier offers a discount such that the purchasing price for all items drops to $295/metric ton if SGM purchases at least 3000 metric tons in an order. An analyst has calculated total annual inventory and setup cost using Q=3000 units as follows:

The analyst concludes that the company should not order 3000 units at a time.

Although the analyst is consistent in his calculation and his conclusion, is the analyst correct in his conclusion? Why or why not?

C(Q) = 10 + - the = $99, 708. 2