Reference no: EM132838620
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 6,500 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.
a. Formulate a linear programming model for this problem.
b. Transform this model into standard form.
c. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met?
d. What is the effect on the optimal solution if the profit per yard of denim is increased from $2.25 to $3.00? What is the effect if the profit per yard of corduroy is increased from $3.10 to $4.00?
e. What would be the effect on the optimal solution if Irwin Mills could obtain only 6,000 pounds of cotton per month?
f. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer.
g. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for corduroy.
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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
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