Question

An artist can sell 20 copies of a painting at $100 each, but for each additional copy he makes, the value of each painting will go down by a dollar. if 22 copies are made, each will sell for $98. How many copies should he make to maximize his sales?

Answer 1

60

Explanation:

The function for the total profit is going to be
`f(x)=(20+x)(100-x)` because the profit is the number of paintings multiplied by the number of dollars per painting, and for each additional painting the cost goes down by one. Multiplying this out, you get the quadratic function
`f(x)=-x^(2)+80x+2000`. We are trying to find the maximum, or the vertex, and we do not care about the y-coordinate of the vertex, which is the dollar amount, we only care about the x coordinate. We can find the x coordinate by using
`-b/2a` , which gives -80/-2 or 40. Now, we must remember that we started with 20 paintings, so adding 20 to 40 we get 60, the final answer.

Answer 2

60

Explanation:

math