Question 114677
The question is not phrased properly.
One formula has -x^2 in it and the repeat of it has x^2.
The question should be "how many hot dogs must he sell to maximize his profit".
{{{P(x)= -x^2+56x+73}}}
x=-1.27456, x=57.27456 quadratic formula (see below)
(-1.27456+57.27456)/2=28 maximum of the graph
By checking the next graph you can see that he can make a profit by selling between 1 and 57 hot dogs and he makes a maximum profit at 28 hot dogs.
{{{graph(500,500,-10,75,-50,1000,-x^2+56x+73)}}}
Ed
*[invoke solve_quadratic_equation -1, 56, 73]