SOLUTION: John owns a hot dog stand. His profit is represented by the equation P = -x^2 + 12x + 44 where P represents profits (in dollars) and x represents the number of hot dogs sold. Wh

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Question 137160: John owns a hot dog stand. His profit is represented by the equation
P = -x^2 + 12x + 44 where P represents profits (in dollars) and x represents the number of hot dogs sold. What is the most he can earn?
I know the answer is 80 but I can't figure out how to set it up. I have tried the quadratic formula. Thanks so much!
Answer by snovember85(4) About Me  (Show Source):
You can put this solution on YOUR website!
You can set up a table of two columns, first column is x values and second column is the function P = -x^2 + 12x + 44.
Plug in x values such that x = 0, 1, 2, ... (the least number of hotdog John can sell is none, so start at 0) and find P.
For example, for x = 0, P = 44; x = 1, P = 55; and so on.
You will see that when you plug in x = 6, P = 80; but when x = 7, P = 79. So the profit decreases when x >= 7. Therefore the most profit John can earn is $80, when 6 hotdogs are sold.