SOLUTION: the barber's profit "p" each week depends on his charge "c" per haircut. it is modeled by the equation p= -200c^2 + 2400c - 4700. what price should he charge for the largest profit

Question 518835: the barber's profit "p" each week depends on his charge "c" per haircut. it is modeled by the equation p= -200c^2 + 2400c - 4700. what price should he charge for the largest profit? what would be his maximum profit?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
the barber's profit "p" each week depends on his charge "c" per haircut. it is modeled by the equation p= -200c^2 + 2400c - 4700. what price should he charge for the largest profit? what would be his maximum profit?
.
By examining the given equation (coefficient associated with the c^2 term), we know that it is a parabola that opens downwards. Therefore, the vertex is the max.
.
what price should he charge for the largest profit?
c = -b/(2a)
c = -2400/(2(-200))
c = -2400/(-400)
c = $6
.
what would be his maximum profit?
plug the value above back into:
p= -200c^2 + 2400c - 4700
p= -200(6)^2 + 2400(6) - 4700
p= -200c^2 + 2400c - 4700
p = $2500

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