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# Charleston Textiles-Linear Programming

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2.Charleston Textiles produces two types of cotton cloth: denim and corduroy. Corduroy is a heavier grade of cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 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 510 yards per month. The mill has 6500 pounds of cotton and 3000 hours of processing time per month. Charleston Textiles makes a profit of \$2.25 per yard of denim and \$3.10 per yard of corduroy. The mill wants to maximize profits.

a.What is the maximum profit given these constraints?
b.How much cotton and processing time are left over at the optimal solution?
c.Is the optimal solution sensitive to changes to profit per yard of cloth?

https://brainmass.com/statistics/linear-regression/charleston-textiles-linear-programming-200456

## SOLUTION This solution is FREE courtesy of BrainMass!

Please see the attached file for complete working of solver in MS Excel to solve linear programming problem.

Solution:

Let x1 be the denim yards produced
Let x2 be the corduory yards produced

Obejective functions is
Maximise Profit P = 2.25 x1+ 3.1x2
Cotton requirement constraint
5x1+7.5 x2 <=6500
Processing time constraint
3 x1+3.2 x2 <=3000
demand for denim is practically unlimited
x1 >=0 or -x1<=0
maximum demand for corduory is 510 yards per month
x2 <=510
off course variables are non negative

In sheet 2, we will find optimal solution by using solver

a. What is the maximum profit given these constraints?
Please refer sheet 2 , maximum profit is \$2607
Denim production is 456 yards and corduory production is 510 yards
b. How much cotton and processing time are left over at the optimal solution?
cotton left = 6500-6105 = 395 pounds
processing time left = nil

c. Is the optimal solution sensitive to changes to profit per yard of cloth?
Yes, optimal solution will be sensitive to changes to profit per yard of cloth

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