The profit in dollars made by selling x bottles of 100 AllNa

The profit, in dollars, made by selling x bottles of 100% All-Natural Certified Free-Trade Organic Sasquatch Tonic is given by P(x) = x2 + 25x 100, for 0 x 35. How many bottles of tonic must be sold to make at least $50 in profit?

Solution

P(x) = x^2 + 25x 100

Profit = $50

50 < -x^2 +25x -100

-x^2 +25x -150=0

solve the equation:

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

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

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

10<=x<=15

So, 10 bottles to 15 bottles must be sold to get a profit of atleast $50