contestada

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?

Respuesta :

adioabiola

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.

MrRoyal

The artist 60 copies should he make to maximize his sales

The artist can sell 20 copies at $100 each.

So, the total sales is:

Total =(20) * (100)

For each additional copy he makes, the value of each painting reduce by a dollar.

So, the total sales becomes

Total = (20 + x) * (100 - x)

Rewrite as:

[tex]y = (20 + x) * (100 - x)[/tex]

Expand

[tex]y = 2000 - 20x + 100x - x^2[/tex]

Evaluate the like terms

[tex]y = 2000 +80x - x^2[/tex]

Differentiate

[tex]y' = 80 - 2x[/tex]

Set to 0

[tex]80 - 2x = 0[/tex]

Collect like terms

[tex]- 2x = -80[/tex]

Divide both sides by -2

[tex]x = 40[/tex]

Recall that the initial copies is 20.

So, the new copies would be:

New = 20 + 40

New = 60

Hence, the artist 60 copies should he make to maximize his sales

Read more about maximum values at:

https://brainly.com/question/10782019