All 5 parts please. Please provide an excel solution.

1. 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: The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of hedium-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 heet the contract at the minimum cost. a) Formulate a linear programming model for this problem. b) Solve the LP model with Excel. c) How much extra (i.e., surplus) high-, medium-, and low-grade aluminum does the company produce at the optimal solution? d) What would be the effect on the optimal solution if the cost of operating mill 1 increased from $6,000 to $6,500 per day? e) Identify and explain the shadow prices for each of the aluminum grade contract requirements