Formulate and solve the model for the following problem Irwi

Formulate and solve the model for the following problem:
Irwin Textile Mills produces two types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 8 pounds of raw cotton per yard, whereas denim requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours of processing time; a yard od 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 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.5 per yards of denim and $3.25 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate the model and put it into standard form. Solve it
a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met?

b. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer.

Solution

Prepare a table with all the given information

Objective is to maximise profit

Corner points feasible are , (510,320) (510,0) (0,1000)

For (510,0) = 1657.5

     (510,320) z = 2457.5

     (0,1000) z = 2500

Hence optimum mix is (0,1000) with max profit = 2500

a) Demand for Corduroy not met at all by optimal solution as x =0

Time = 3000

No time is extra

Cotton required = 6000

500 yards cotton left.

-------------------------------------------------

b) As time is fully utilised he can obtain additional processing time to utilize the extra cotton and maximise profit.