Problem:
Barrows Textile Mills produces two types of cotton cloth: denim and corduroy. Corduroy is a heavier grade of cotton cloth and requires 7.5 pounds of raw cotton per yard. On the other hand, denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time while a yard of denim requires 3.0 hours. The demand for denim is infinite while 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 makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. How many yards of each type of cloth should they produce to maximize profit?
1. Formulate and solve a linear programming model for this problem.