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. Thus, if 22 copies are made, each will sell for $98. How many copies should he make to maximize his sales?

Answer 1

Answer:

40 more paintings in order to maximize sales making a total of 60 paintings

Step-by-step explanation:

Let x= no.of copies above 20

Total Sales(x) = (number of copies)(price per copy)

Sales (x)= (20 +x)(100 –x)

Open bracket

=1200-20x+100x-x^2

=1200+80x-x^2

Derivative of the sales

80-2x=0

80=2x

Divide both sides by 2

40=x

Because Sales(x)= –2, this is maximal by the second derivative test

The artist should make 40 more paintings in order to maximize sales making a total of 60 paintings.