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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

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

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 73P
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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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