Question 533657
{{{P = -x^2+56x+77}}} This is a quadratic equation which, when graph, will give a parabola that opens downward. (Note the negative {{{x^2}}} term)
The x-coordinate of the maximum of this parabola, and thus the maximum number of hotdogs, is given by:
{{{x = -b/2a}}} where: a = -1 and b = 56, so...
{{{x = -56/2(-1)}}}
{{{x = 28}}}
John must sell 28 hotdogs to earn the most profit.
The maximum profit, {{{P[m]}}}, can be found by substituting {{{x = 28}}} into the given equation for profit.
{{{P[m] = -(28)^2+56(28)+77}}}
{{{P = 861}}}