Question

How do I find the ticket price so that I can also find the maximum profit?

Answer 1

We have a quadratic equation of the form:

$f(x)=at^2+bt+c$

Let:

P(t) = Profit

$\begin{gathered} P(t)=-t^2+27t-112 \\ _{\text{ }}where\colon \\ a=-1 \\ b=27 \\ c=-112 \end{gathered}$

Using the formula provided by the problem:

$\begin{gathered} h=-\frac{b}{2a} \\ so\colon \\ h=-\frac{27}{2(-1)} \\ h=13.5 \end{gathered}$

Answer:

$13.5