Barrows Textile Mills produces two types of cotton cloth—denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 kilograms of raw cotton per meter, whereas denim requires 5 kilograms of raw cotton per meter. A meter of corduroy requires 3.2 hours of processing time; a meter of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 meters per month. The manufacturer has 6500 kilograms of cotton and 3000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per meter of denim and $3.10 per meter of corduroy. The manufacturer wants to know how many meters of each type of cloth to produce to maximize profit. 

a.  Formulate and solve a linear programming model for this problem.
b. Solve this model using the graphical method.