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Question 1 United Aluminum Company produces three grades (high, medium, and low) of alumnimum at two mills. Each mill has a different production capacity (in tons per day) for each grade, as follows: Mill 1 Mill 2 Aluminum grade High Medium Low 6 2 2 2 4 10 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 1 and $7,000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost. a. Formulate the linear programming model for this problem and solve graphically. Confirm your solution using Solver. b. How much extra (i.e. surplus) high-, medium-, and low-grade aluminum does the company produce at the optimal solution? c. What would be the effect on the optimal solution if the cost of operating mill 1 increased from $6,000 to $7,500 per day? d. What would be the effect on the optimal solution obtained in part c, if the company could supply only 10 tons of high-grade aluminum? e. In the original model (the one you formulated in part a): what is the shadow price for each of the three aluminum grades? f. In the original model: what is the sensitivity range for the objective function coefficients