Modern Textile Mills produces two types of cotton cloth, denim and corduroy. Corduroy is a heavier grade of cotton cloth and requires 5 pounds of raw cotton per yard, whereas denim requires 3 pounds of raw cotton per yard. A yard of corduroy requires 3.6 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 20 yards per month. The manufacturer has 150 pounds of cotton and 90 hours of processing time available each month. The manufacturer wants to make sure that it produces denim at least as twice the size of the corduroy produced. The manufacturer makes a profit of $5.00 per yard of corduroy and $2.50 per yard of denim. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit.

a. Formulate an LP model to find the number of units of each product to be produced to maximize the profit (CLEARLY WRITE OUT DECISION VARIABLES, OBJECTIVE FUNCTION & CONSTRAINTS)

b. Find the optimal solution using graphical approach (please make sure it is clear)