12. United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade, as follows: Aluminum Grade High Medium Low Mill 6 2 4 The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5 tons of low-grade aluminum. It costs United $6,000 per day to operate mill I and $7,000 per day to operate mill 2. The company wants to know the number of days to operate each mill to meet the contract at the minimum cost. Formulate a linear programming model for this problem.