We have a quadratic equation of the form:
[tex]f(x)=at^2+bt+c[/tex]
Let:
P(t) = Profit
[tex]\begin{gathered} P(t)=-t^2+27t-112 \\ _{\text{ }}where\colon \\ a=-1 \\ b=27 \\ c=-112 \end{gathered}[/tex]
Using the formula provided by the problem:
[tex]\begin{gathered} h=-\frac{b}{2a} \\ so\colon \\ h=-\frac{27}{2(-1)} \\ h=13.5 \end{gathered}[/tex]
Answer:
$13.5
