(Solution) - A large chemical company in Green River Wyoming mines soda -(2025 Original AI-Free Solution)

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A large chemical company in Green River, Wyoming, mines soda ash used in glass manufacturing. Soda ash is* sold to a number of manufacturers through annual contracts. The glass companies release their requests for soda ash against their contracts. The mining company sees demand in the form of rail-car quantities. A typical week shows demand to be normally distributed at 40 rail-car loads plus or minus 10 cars. They estimate the standard deviation at (max cars - min cars)/6 = (50 - 30)/6 = 3.33 cars.
Soda ash is valued at $30 per ton, and an average rail-car load is 90,000 lb of product. Annual carrying cost for the company is 25 percent per year. Setup costs at the mine are estimated to be $500 per order. It takes one week to produce the product and/or secure the rail-cars for shipment. A 90 percent in-stock probability during the lead time is desired.
a. The company must call for cars from the railroad to fill orders. How many cars should be requested at a time? (Remember: One ton is 2,000 lb.)
b. At what quantity of soda ash remaining in inventory should the request for cars be made?