The Pumpkin Patch Doll Company has detrmined that the profit the company makes on Pumpkin Patch Dolls if given by the equation y=3x2 + 720 x - 17800, where y is the profit measured in dollars and x is the number of Pumpkin Patch dolls. Find the number of dolls that will maximize the company's profit. What is the profit?
You have a sign mistake. Your profit goes to infinity as number of dolls go to infinity. However here is the method.
y = 3 x^2 + 720 x -17800
3 x^2 + 720 x = y + 17800
x^2 + 240 x = y/3 + 5933.33
x^2 + 240 x + 14400 = y/3 + 20333
(x+120)^2 = y/3 + 20333
minimum at x = -120
this is nonsense because your problem statement has a sign error.