4. Southern Sporting Goods Company makes basketballs and footballs. Each product
ID: 3120589 • Letter: 4
Question
4. 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 (ft.2)
Basketball 3 4
Football 2 5
Total resources available 500 lb. 800 ft.2
Each basketball produced results in a profit of $12, and each football earns $16 in profit.
I have formulated and solved the problem by using QM for Windows. The output from QM for Windows is displayed below.
Linear Programming Results:
Variable Status Value
Basketball NONBasic 0
Football Basic 160
slack 1 Basic 180
slack 2 NONBasic 0
Optimal Value (Z) 2560
Original Problem w/answers:
Basketball Football RHS Dual
Maximize 12 16
Rubber 3 2 <= 500 0
Leather 4 5 <= 800 3.2
Solution-> 0 160 Optimal Z-> 2,560
(a) Determine the optimal solution from the output from QM for Windows.
(b) Make a recommendation to the company based on the output from QM for Windows.
Explanation / Answer
a>
The optimal solution is Basketball = 0, Football =160 , these are the amount of each product that will yield the maximum total profit of 2560 subject to the constraints given.
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