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 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 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. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit.

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 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 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. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 16P

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Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such as, requires 8 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.6 hours of processing time; a yard of denim requires 8 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 600 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 $3.0 per yard of denim and $4.0 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. How much extra cotton, processing time, and the demand for corduroy are left over at the optimal solution after formulating a linear programming model? What is the effect on the optimal solution if the profit per yard of denim is increased from$3.0 to $4.0?
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Irwin 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 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 manufacturer has 5,500 pounds of cotton and 3,000 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. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. If Irwin Mills could obtain only 5,000 pounds of cotton per month, at the optimal solution, the value of X2 is: (refer to slides #17-19 for the clue) Question 3 options: 456 510 1,000 0