SOLUTION: I have several word problems to solve but this is the first one. John owns a hotdog stand. His profit is represented by the equation P(x)=-x^2+12x+46, with P being profits and the

Algebra ->  Permutations -> SOLUTION: I have several word problems to solve but this is the first one. John owns a hotdog stand. His profit is represented by the equation P(x)=-x^2+12x+46, with P being profits and the      Log On


   

Question 136931: I have several word problems to solve but this is the first one. John owns a hotdog stand. His profit is represented by the equation P(x)=-x^2+12x+46, with P being profits and the x the number of hotdogs sold. What is the most he can earn?
Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
The most he can earn is basically the maximum value of the function.
And the maximum occurs at the vertex of this parabola.
The given equation is P(x) = -x^2+12x+46,
The x coordinate of the vertex = %28-b%29%2F%282%2Aa%29
= %28-12%29%2F%282%2A%28-1%29%29
= 6
Plugging this value of x in P(x), P(6)= -36 + 72 + 46
= 82
Thus the most he can earn is 82
Good luck!!!
dolly