United Aluminum Company of Cincinnati produces three grades(high medium low) of

United Aluminum Company of Cincinnati produces three grades(high medium low) of aluminum at two mills. Each mill has adifferent production capacity (in tons per day) for each grade asfollows: Mill Aluminum Grade 1 2 High 6 2 Medium 2 2 Low 4 10 Thecompany has contracted with a manufacturing firm to supply at least12 tons of high-grade aluminum 8 tons of medium-grade aluminumand 5 tons of low-grade aluminum. It costs United $6000 per day tooperate mill 1 and $7000 per day to operate mill 2. The companywants to know the number of days to operate each mill to meet thecontract at minimum cost. a. Formulate a linear programming modelfor this problem. b. Solve this problem by using the computer.