Question

Ashton manages a company that makes and sells two kinds of stereos, the Boomer and the Jammer. Each

Boomer takes 9 hours to create the plastic parts, 4 hours to create the electronics, and 4 hours for
assembly. Each Jammer requires 6 hours to create the plastic parts, 3 hours to create the electronics, and
8 hours for assembly. The factory can handle a maximum of 2295 hours to create the plastic parts, 1038
hours to create the electronics, and 1808 hours for assembly each week. If each Boomer generates $12 in
profit, and each Jammer generates $9, how many of each of the stereos should Ashton have the company
make and sell each week to earn the most profit?
Boomer:
Jammer:
Best profit:

Answer 1

To earn the most profit, Ashton should produce and sell 152 Boomer stereos and 254 Jammer stereos each week, resulting in a profit of $4,312.

Step-by-step explanation:

To maximize profit, we need to determine how many units of each stereo Ashton should produce and sell each week. Let's use the following variables:

B = number of Boomers produced and sold

J = number of Jammers produced and sold

The time constraints can be written as inequalities:

9B + 6J ≤ 2295 (for plastic parts)

4B + 3J ≤ 1038 (for electronics)

4B + 8J ≤ 1808 (for assembly)

Since we want to maximize profit, our objective function is:

12B + 9J

We can solve this linear programming problem graphically or using the simplex method. The optimal solution is B = 152, J = 254, and the best profit is $4,312.