Discuss the following:
Q1: 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 available are as follows.
Resource Requirements 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.
a. Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profits.
b. Transform this model into standard form.
Q2: Solve the model formulated in problem #5 for the Southern Goods Company graphically.
a. Identify the amount of unused resources (i.e., slack) at each of the graphical 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?
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?