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 43.5 pounds of foam and 110 labor-hours a week. Use the simplex method to determine the optimal production schedule so as to maximize profits. Show that the geometric method gives the same solution.

maximum profits = $508 when 24 basketballs are produced and 224 footballs are produced

Step-by-step explanation:

Basketball : uses 4 ounces of foam, 20 minutes labor and makes a profit of $2.50

Football : uses 3 ounces of foam, 30 minutes of labor and makes a profit of $2

Available materials:

43.5 pounds of foam , 110 labor-hours a week  

A ) using the simplex method to determine the optimal production schedule  to maximize profits

number of basketballs produced = x

number of football produced = y

we have to determine constraints based on the available information

Z = 2.5 x + 2 y  ( Profit function )

4 x + 3 y ≤ 43.5 * 16( pounds of foam function )

20 x + 30 y ≤ 110 *16 ( labor-hours a week function )

x ≥ 0

y ≥ 0

Therefore this equation can be written as

Z ( maximization of profit ) = 2.5 x + 2 y is subject to

4 x + 3 y ≤ 696

20 x + 30 y ≤  1760

x ≥ 0

y ≥ 0

attached is the remaining detailed solution

addition

step-by-step explanation: