Question

A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor and brings a profit of $2.50. The football uses 3 ounces of foam and 30 minutes of labor and brings a profit of $2. The manufacturer has available 48 pounds (768 ounces) of foam, and 120 labor-hours a week.

Use the simplex method to determine the optimal production schedule so as to maximize profits.

Answer 1

(24, 224 ) i.e. 24 basketball and 224 footballs

Explanation:

Basketball :

uses 4 ounces of foam

20 minutes of labor

profit = $2.50

Football :

uses 3 ounces of foam

30 minutes of labor

profit = $2

Manufacturer has :

768 ounces of foam , 120 labor hours per week,

using the simplex method to determine the optimal production schedule so as to maximize profits

lets assume

x = number of basketball

y = number of footballs

maximize = 2.5 x + 2y from a linear programming problem

attached below is the detailed solution