NUMBER 10, 11, 13. PLEASE SHOW ALL WORK.

PROBLEMS 101 manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. a. Formulate a linear programming model for this problem. b. Transform this model into standard form. 10. Solve the model formulated in Problem 9 for Irwin Textile Mills graphically. a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met? b. What is the effect on the optimal solution if the profit per yard of denim is increased from $2.25 to $3.00? What is the effect if the profit per yard of corduroy is increased from $3.10 to $4.00? c. What would be the effect on the optimal solution if Irwin Mills could obtain only 6,000 pounds of cotton per month? 11. Solve the linear programming model formulated in Problem 9 for Irwin Mills by using the computer. a. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. b. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for corduroy. 12. United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum two mills. Each mill has a different production capacity (in tons per day) for each grade, as follows: Mill Aluminum Grade 1 2 High 6 2 2 Medium Low 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 to meet the contract at the minimum cost. Formulate a linear programming model for this problem. 13. Solve the linear programming model formulated in Problem 12 for United Aluminum Company graphically. a. How much extra (i.e., surplus) high-, medium-, and low-grade aluminum does the company produce at the optimal solution? b. 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? c. What would be the effect on the optimal solution if the company could supply only 10 tons of high-grade aluminum? 14. Solve the linear programming model formulated in Problem 12 for United Aluminum Company by using the computer. a. Identify and explain the shadow prices for each of the aluminum grade contract requirements. b. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values. c. Would the solution values change if the contract requirements for high-grade aluminum were increased from 12 tons to 20 tons? If yes, what would the new solution values be