Question 166842
To earn money, his profits have to be positive.
{{{P(x)>=0}}}
Let's find the point where the profits equal zero.
From that point on, his profit will be positive.
{{{P(x)=0}}}
{{{-x^2+62x+79=0}}}
{{{ graph( 300, 300, -10, 50, -50, 1500, -x^2+62x+79) }}} 
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Check the equation. 
John makes a $79 profit selling 0 hot dogs, that can't be right. 
Also, when he sells more than a certain number (63), his profits become negative, that doesn't make sense either.
Check and re-post the problem.