Formulate and solve the model for the following problem: (Solver)

Irwin Textile Mills produce two types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton cloth and as such requires 7.5 pounds of raw cotton per yard. Whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6500 pounds of cotton and 3000 hours of processing time available each month. The manufacturer wants to know how many of each type of cloth to produce to maximize profit.

Answer the following questions:

1. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met?
2. 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 of the profit per yard of corduroy is increased from $3.10 to $4.00?
3. What would be the effect on the optimal solution if Irwin Mills could contain only 6000 pound of cotton per month?
4. Continuing the model answer the following:
   1. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer.
   2. 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.

Irwin textile mills (a) Corduroy 3.1 denim 2.25 Profits for each product Resources Left over 5