SOLUTION: Emilia manages a company that makes and sells two kinds of speakers, the Boomer and the Rocker. Each Boomer takes 10 hours to create the plastic parts, 5 hours to create the electr

Question 1205168: Emilia manages a company that makes and sells two kinds of speakers, the Boomer and the Rocker. Each Boomer takes 10 hours to create the plastic parts, 5 hours to create the electronics, and 6 hours for assembly. Each Rocker requires 6 hours to create the plastic parts, 6 hours to create the electronics, and 4 hours for assembly. The factory can handle a maximum of 3020 hours to create the plastic parts, 1848 hours to create the electronics, and 1840 hours for assembly each week. If each Boomer generates $8 in revenue, and each Rocker generates $11, how many of each of the speakers should Emilia have the company make and sell each week to earn the most revenue?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of boomer speakers.
y = number of rocker speakers.

plastic parts:
10x + 6y <= 3020
electronics:
5x + 6y <= 1848
assembly:
6x + 4y <= 1840
revenue:
8x + 11y = objective function to maximize.

using the desmos.com/calculator, you would:
graph the opposite of the inequalities.
the area that is not shaded is the region of feasibility.
the corner points of that region are where the maximum revenue lies.

the graph looks like this:

the maximum revenue is at the point (0,308) where the revenue = 8 * 0 + 11 * 308 = 3388.
all the constraints are satisfied.
plastic parts:
10x + 6y = 10 * 0 + 6 * 308 = 1848 <= 3020
electronics:
5x + 6y = 5 * 0 + 6 * 308 = 1848 <= 1848
assembly:
6x + 4y = 6 * 0 + 4 * 308 = 1232 <= 1840

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