ST9.1 Cost Minimization. Idaho Natural Resources (INR) has two mines with different production capabilities for producing the same type of ore. After mining and crushing, the ore is graded into three classes: high, medium, and low. The company has contracted to provide local smelters with 24 tons of high-grade ore, 16 tons of medium-grade ore, and 48 tons of low-grade ore each week. It costs INR $10,000 per day to operate mine A and $5,000 per day to run mine B. In a day's time, mine A produces 6 tons of high-grade ore, 2 tons of medium-grade ore, and 4 tons of low-grade ore. Mine B produces 2, 2, and 12 tons per day of each grade, respectively. Management's short-run problem is to determine how many days per week to operate each mine under current conditions. In the long run, management wishes to know how sensitive these decisions will be to changing economic conditions.
A report prepared for the company by an independent management consultant addressed the company's short-run operating concerns. The consultant claimed that the operating problem could be solved using linear programming techniques by which the firm would seek to minimize the total cost of meeting contractual requirements. Specifically, the consultant recommended that INR do the following:
Minimize Total Cost = $10,000A + $5,000B
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