Question 224713
Assume the profit earned by an artist in any given year is governed by the function:
P(n) = -2n^2 + 20n – 30
where n represents the number of paintings sold and P (in thousands of dollars) represents the profit. 
How many paintings should be sold to create a maximum profit?
:
This is a quadratic equation; find the axis of symmetry:
This formula x = -b/(2a)
In this equation x=n; b=20; a=-2
n = {{{(-20)/(2*-2)}}}
n = {{{(-20)/(-4)}}}
n = +5 paintings for max profit
:
What is the maximum profit?
Substitute 5 for n in the original equaiton
p(n) = -2(5^2) + 20(5) - 30
p(n) = -2(25) + 100 - 30
p(n) = -50 + 100 - 30
p(n) = $20 thousand profit