SOLUTION: The barbers profit p each week depends on his charge c per haircut. It is modeled by the equation p=-200c^2+2400c-4700. Sketch the graph of the equation. What price should he charg

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The barbers profit p each week depends on his charge c per haircut. It is modeled by the equation p=-200c^2+2400c-4700. Sketch the graph of the equation. What price should he charg      Log On


   

Question 1206403: The barbers profit p each week depends on his charge c per haircut. It is modeled by the equation p=-200c^2+2400c-4700. Sketch the graph of the equation. What price should he charge for the largest profit?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the profit equation is p = -200 * c^2 + 2400 * c - 4700
p is the profit
c is the cost
maximum profit is at x = -b/2a.
a is the coefficient of the x^2 term.
b is the coefficient of the x term.
in this equation, you get maximum profit at x = -2400 / (2 * -200).
solve for x to get x = 6.
maximum profit is at f(6).
f(6) = -200 * 6^2 + 2400 * 6 - 4700 = 2500.
here is the graph with the maximum profit at (6,2500) shown.