## Week 7 homework

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 3.7 Football 1.5 5.2 Total resources available 600 900

a. Find the optimal solution. b. What would be the effect on the optimal solution if the profit for the basketball changed from \$11 to \$12? c. What would be the effect on optimal solution if 400 additional pounds of rubber could be obtained? What would be the effect if 600 additional square feet of leather could be obtained? 2. A company produces two products, A and B, which have profits of \$9 and \$7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows:
Product
Resource Requirements per Unit Line 1 Line 2 A 11 5 B 6 9 Total Hours 65 40

a. Formulate a linear programming model to determine the optimal product mix that will maximize profit.
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b. What are the sensitivity ranges for the objective function coefficients? c. Determine the shadow prices for additional hours of production time on line 1 and line 2 and indicate whether the company would prefer additional line 1 or line 2 hours. 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 it into standard form. Solve it