A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor a
nd 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.
1 answer:
Answer:
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
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