Applied Optimization: Videos & Practice Problems

A company is planning to send a shipment over a distance of $300$ miles. The truck consumes diesel at a rate described by the function $d\left(v\right)=\frac{v(90-v)}{70}$, where $d$ is the diesel efficiency in mi/gal and $v$ is the speed in mph. The diesel costs $\mathrm{\backslash (}3$ per gallon, and the driver's wage is $\mathrm{\backslash )}25$ per hour. Should the speed that minimizes the cost be increased or decreased if the distance is increased from $300$ miles to $400$ miles? Justify your answer.