An artist makes a profit of (500p - p^2) dollars from selling p paintings. What is the fewest number of paintings the artist can sell to make a profit of at least $60,000?

Question

Don't know how to even set it up

Answer 1

just use what you are given:

500p - p^2 >= 60000

Now, just from what you know about parabolas, you know that the parabola opens downward. So, the portion of the curve above a horizontal line (here, y=60000) will lie between the roots of

500p - p^2 - 60000 = 0
The roots are 200, 300.

So, selling anywhere between 200 and 300 paintings will result in a profit of at least 60,000.

See

http://www.wolframalpha.com/input/?i=500p+-+p^2+%3E%3D+60000

Answer 2

150