[25 points] Irwin Textile Mills produces two types of cotton cloth- denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 8.0 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time while a yard of denim requires 3.1 hours. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.45 per yard of denim and $3.15 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. [6 points] Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? [7 points] Confirm graphically that the solution to part a maximizes their profit. [4 points] Starting with the optimal solution to part a, use the SolverTable add-in to see what happens to the decision variables and the optimal profit when the profits per yard of denim varies from $1.70 to $3.20 in $.25 increments. Track the changes in the decision variables and the objection function. Are the changes in optimal profit linear with respect to changes in the unit profit of denim? [4 points] Starting with the optimal solution to part a, use the SolverTable add-in to see what happens to the decision variables and the optimal profit when the profits per yard corduroy varies from $2.25 to $4.05 in $.30 increments. Track the changes in the decision variables and the objection function. Are the changes in optimal profit linear with respect to changes in the unit profit of corduroy? [4 points] Starting with the optimal solution to part a, use the SolverTable add-in to see what happens to the decision variables and the optimal profit when the availability of cotton varies by a factor of (1 + k) while the availability of processing time varies by a factor of (1-k). In particular, let k vary from -0.3 (-30%) to 0.3 (30%) in increments of 0.05 (5%) and track the changes in the decision variables and the objection function. Are the changes in optimal profit linear with respect to changes in k?

[25 points] Irwin Textile Mills produces two types of cotton cloth - denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 8.0 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time while a yard of denim requires 3.1 hours. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.45 per yard of denim and $3.15 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. [6 points] Create a spreadsheet model for this problem and solve it using Solver. What is the optimal solution? [7 points] Confirm graphically that the solution to part a maximizes their profit. [4 points] Starting with the optimal solution to part a, use the SolverTable add-in to see what happens to the decision variables and the optimal profit when the profits per yard of denim varies from $1.70 to $3.20 in $.25 increments. Track the changes in the decision variables and the objection function. Are the changes in optimal profit linear with respect to changes in the unit profit of denim? [4 points] Starting with the optimal solution to part a, use the SolverTable add-in to see what happens to the decision variables and the optimal profit when the profits per yard corduroy varies from $2.25 to $4.05 in $.30 increments. Track the changes in the decision variables and the objection function. Are the changes in optimal profit linear with respect to changes in the unit profit of corduroy? [4 points] Starting with the optimal solution to part a, use the SolverTable add-in to see what happens to the decision variables and the optimal profit when the availability of cotton varies by a factor of (1+k) while the availability of processing time varies by a factor of (1k). In particular, let k vary from -0.3 (30%) to 0.3(30%) in increments of 0.05(5%) and track the changes in the decision variables and the objection function. Are the changes in optimal profit linear with respect to changes in k ? fx Problem 1 \begin{tabular}{|l|l|l|l|l|l|} \hline B & C & D & E & F & G \\ \hline \end{tabular} 1 2