Question

An artist can sell 20 compies of a painting for $100 each, but for each additional copy he makes the value of each painting will go down by 1 dollar. How many copies should he make to maximize the profit?

Answer 1

40 copies for $3000

Explanation:

First: The Equation

y=(20+x)(100-x)

This shows how for every new painting, the price will go down.

y=2000+80x-x²

Convert it to standard form: ax²+bx+c

You can now choose to graph it or find the vertex form. For the limit of time, I will just use a graph.

The vertex, (40,3000), is your answer, where the x value is the number of paintings and the y value the money made.