Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such as, requires 8 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.6 hours of processing time; a yard of denim requires 2.8 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 600 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $3.0 per yard of denim and $4.0 per yard of corduroy. The 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) Solve the problem by using the computer.

(c) How much extra cotton, processing time, and the demand for corduroy are left over at the optimal solution in (a)?

(d) Identify the sensitivity ranges of the profits of denim and corduroy, respectively, at the optimal solution in (a).

(e) What is the effect on the optimal solution if the profit per yard of denim is increased from $3.0 to $4.0?