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QUESTION 12 A mining company owns 3 different mines (North, South, and West mines) that produce 3 different grades of iron (low-grade, medium-grade, and high- grade). The company requires at least 25 tons of low-grade iron, 18 tons of medium-grade iron, and 12 tons of high-grade iron in order to meet its supply requirements. The North Mine costs $10,000 per day of mining and in a day of mining it produces 4 tons of low-grade iron, 1 ton of medium-grade iron, and 1 ton of high-grade iron. The South Mine costs $15,000 per day of mining and in a day of mining it produces 1 ton of low-grade iron, 3 tons of medium grade iron, and 2 tons of high-grade iron. The West Mine costs $18,000 per day of mining and in a day of mining it produces 3 tons of low-grade iron, 3 tons of medium-grade iron, and no high-grade iron. Suppose x is the number of days that the North Mine is operational, y is the number of days that the South Mine is operational, and z is the number of days у that the West Mine is operational. If the company wants to minimize its total cost while satisfying its supply requirements, fill in the blanks below to formulate this situation as a linear program. (Make sure to input only numbers, do not include any dollar signs, commas, periods, or other symbols in your answers) Minimize X + y + Z Subject to: X+ y + z 25 X + y + Z > 18 X + y + z 12 X2 ya Z2