MAT540Week 7 HomeworkChapter 31. Southern Sporting Good Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. The resource requirements for each product and the total resources available are as follows:Resource Requirements per UnitProductRubber (lb.)Leather (ft2)Basketball34Football25Total resources available500 lb.800 ft2a. State the optimal solution.b. What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? What would be the effect if the profit for a football changed from $16 to $15?c. What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 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:Hours/ UnitProductLine 1Line2A124B48Total Hours6040a. Formulate a linear programming model to determine the optimal product mix that will maximize profit.b. Transform this model into standard form.3. Solve problem 2 using the computer.a. State the optimal solution.b. What would be the effect on the optimal solution if the production time on line 1 was reduced to

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