Answer:
using solver, the optimal solution is 6,666P₁ or process 1 should work for 6,666 hours during the year.
Total production = 6,666 x 3 = 19,998 ounces of perfume.
Total revenue = 19,998 x $5 = $99,990
Total costs = (6,666 x $3 per labor hour) + (6,666 x 2 x $2 per unit of chemicals) = $46,662
Operating income = $53,328
Step-by-step explanation:
Variables:
P₁ = number of hours in process 1
P₂ = number of hours in process 2
P₁ yields 3 ounces of perfume
P₂ yields 5 ounces of perfume
both are sold at $5 per ounce
15P₁ + 25P₂
labor usage:
(1P₁ + 2P₂) x $3
3P₁ + 6P₂
chemicals usage:
(2P₁ + 3P₂) x $2
4P₁ + 6P₂
Profit = 15P₁ + 25P₂ - (3P₁ + 6P₂) - (4P₁ + 6P₂) = 8P₁ + 13P₂
so we need to maximize 8P₁ + 13P₂
the constraints are:
3P₁ + 6P₂ ≤ 20,000
4P₁ + 6P₂ ≤ 35,000
P₁, P₂ ≥ 0
using solver, the optimal solution is 6,666P₁ or process 1 should work for 6,666 hours during the year.
Total production = 6,666 x 3 = 19,998 ounces of perfume.
Total revenue = 19,998 x $5 = $99,990
Total costs = (6,666 x $3 per labor hour) + (6,666 x 2 x $2 per unit of chemicals) = $46,662
Operating income = $53,328
