Mat 540 Week 7 Homework Chapter 3

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1. Southern Sporting Good Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. Each basketball produced results in a profit of $11 and each football earns $15 in profit. The resource requirements for each product and the total resources available are as follows:
Product Resource Requirements per Unit
Rubber (lb.) Leather (ft2)
Basketball 2.8
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3. 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 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.
4. The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The Bradleys’ have a budget of $52,500 for next

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