Answer
The dot product is $\$1617$.
Work Step by Step
The dot product of $\mathbf{v}$ and $\mathbf{w}$ is:
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=\left( 240\mathbf{i}+300\mathbf{j} \right)\cdot \left( 2.90\mathbf{i}+3.07\mathbf{j} \right) \\
& =240\left( 2.90 \right)+300\left( 3.07 \right) \\
& =696+921 \\
& =1617
\end{align}$
This means that by selling $240$ gallons of regular gas for a price of $\$2.90$ per gallon and $300$ gallons of premium gas at a price of $\$3.07$ per gallon has a total revenue of $\$1617$.
