Question 1058425
The profit function is:


P(x) = R(x) - C(x)


P(x) = (1200x - x^2) - (3100 + 20x)


P(x) = -x^2 + 1200x - 20x - 3100


P(x) = -x^2 + 1180x - 3100


This is the equation of a parabola that opens downward. The maximum value of the profit
corresponds to the vertex of the parabola.


The x-coordinate of the vertex is:


x = -b/2a = (-1180) / (-1*2) = 590


The function value at the vertex is then:


P(590) = -(590)^2 + 1198(590) - 3100


P(590) = 345,000


Solution:


Total profit = -x^2 + 1180x - 3100


Maximum profit = 345,000, at x = 590