The profit in dollars made by selling x bottles of wine is g

The profit, in dollars, made by selling x bottles of wine is given by P(x)=-x^2+25x-100, for 0<x<35.

How many bottles of wine must be sold for at least $50 profit?

Solution

Solution:- Given P = x² +25 x -100

Profit for x = 0

P(0) = 0 +0 - 100 = -100 dollars

It means loss = 100 dollars for not selling any wine bottle

for x = 35

-(35)^2 + 25 X 35 -100 = -450 dollars

50 = -x^2 +25 x -100

-x^2 +25 x -150 = 0

x^2 -25 x +150 = 0

x^2 -15 x -10x +150 =0

x(x-15) -10(x-15)

(x-15)(x-10) =0

x =15, 10