Question

Creative Sports Design (CSD) manufactures a standard-size racket and an oversize racket. The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy that was invented by the firm’s founder. Each standard-size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two-week production period only 80 kilograms of the alloy are available. Each standard-size racket uses 10 minutes of manufacturing time and each oversize racket uses 12 minutes. The profit contributions are $10 for each standard-size racket and $15 for each oversize racket, and 40 hours of manufacturing time are available each week. Management specified that at least 20% of the total production must be the standard-size racket. How many rackets of each type should CSD manufacture over the next two weeks to maximize the total profit contribution? Assume that because of the unique nature of their products, CSD can sell as many rackets as they can produce.

Answer 1

Let       S = number of standard size rackets

O = number of oversize size rackets

 

Max	10S	+	15O
s.t.
	0.8S	-	0.2O	≥	0	% standard
	10S	+	12O	≤	4800	Time
	0.125S	+	0.4O	≤	80	Alloy

            S, O, ≥ 0

 

 Let       S = number of standard size rackets

O = number of oversize size rackets

 

Max	10S	+	15O
s.t.
	0.8S	-	0.2O	≥	0	% standard
	10S	+	12O	≤	4800	Time
	0.125S	+	0.4O	≤	80	Alloy

            S, O, ≥ 0