Problem 4 ( 30 points) Southern Sporting Goods Company makes baskotballs and footballs. Each product is produced from two resources - rubber and leather. To prodnce a basketball, it requires 3lb. rubber and 4 squared ff. leather. To produce A football, it requires 2lb. rubber and 5 squared it. leather. There are 500lb, rubber and 800 squared f. available, Each basketball produeed results in a proft of $12, and each football carns $16 in profit. a. Formulate a linear programming model to determine the number of basketballs-and footballs to produce in order to maximize profit. b. Solve it graphically. Identify the amount of umused resouroes (Le., slack) at each of the graphical extreme points. c. What woukd 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 foot bull chisged from $16 to $15 ? d. What would be the effect on the optimal sodution if 500 additioual poundr of rubber condal be obtained? What would be the effect if 500 additional square feet of leather could be obtained? e. Determine the sensitivity ranger for the objective function coefficients and constraint quantity values. taing graphical analysis. f. Verify the sensitivity ranges detertinimed in (e) by wsing the computer. g. Using the computes, determite the shadow prices for the rosouros and explain their mesuing