The Charm City Mining Company owns two mines, each of which produces three grades of ore— high, medium, and low. The company has a contract to supply a smelting company with at least 100 tons of high-grade ore, 110 tons of medium-grade ore, and 120 tons of low-grade ore. Each mine produces a certain amount of each type of ore during each hour that it operates. Mine 1 produces 6.2 tons of high-grade ore, 3.2 tons of medium-grade ore, and 4.5 tons of low grade ore per hour. Mine 2 produces 3.5, 4.1, and 8 tons, respectively, of high-, medium-, and low-grade ore per hour. It costs the company $350 per hour to operate mine 1, and it costs $250 per hour to operate mine 2. The company wants to determine the number of hours it needs to operate each mine so that its contractual obligations can be met at the lowest cost.
(a) Define the decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.