profit is surplus amount from the costs and selling price
so.. in short, profit is Revenue - Costs, whatever is left, is profit
thus the profit function or P(t) will be R(t) - C(t)
thus [tex]\bf \begin{cases}
R(t)=5t^2+t\\\\
C(t)=4t^2+9t
\end{cases}\qquad
\begin{array}{llll}
P(t)=(5t^2+t)\quad -\quad (4t^2+9t)\\\\
P(t)=5t^2-4t^2+t-9t\\\\
P(t)=t^2-8t
\end{array} [/tex]
solve for "t", any value greater than 0, is profit
