Question: The Southern Sporting Goods 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 are as follows:

Resources Per Unit

Product Rubber (lb) Leather (ft2)

Basketball 3 4

Football 2 5

Total Resources Available 500 lb 800 ft2

Each basketball produced results in a profit of $12 and each football earns $16 in profit. Formulate a linear programming model to determine the number of basketballs and transform the model into standard form.

a) Solve the model formulated for problem 5 graphically by providing the solution vertices, choose the optimum solution, and identify the amount of unused resources (i.e., slack) at each of the extreme points.

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 (assume the profit for a basketball has been reset to $12)?

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? (Again, each question should be treated separate.