Answer
The dot product is $\$1440$.
Work Step by Step
The dot product of $\mathbf{v}$ and $\mathbf{w}$ is:
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( 180\mathbf{i}+450\mathbf{j} \right)\cdot \left( 3\mathbf{i}+2\mathbf{j} \right) \\
& =180\left( 3 \right)+450\left( 2 \right) \\
& =540+900 \\
& =1440.
\end{align}$
This means that by renting $180$ one-day videos at $\$3$ each and $450$ 3-day videos at $\$2$ each, the total collected by the video store is $\$1440$.
