Review question

What's the most economical speed for this ship's journey? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7280

Question

The cost of running a cargo ship is $£150$ a day for wages and other crew expenses and $£\dfrac{8v^2}{3}$ a day for fuel and maintenance, where $v$ is the steady speed in $\quantity{}{km/h}$. Find in terms of $v$ how many days a voyage of $\quantity{2400}{km}$ takes and hence obtain a formula for the total cost of the whole voyage.

Deduce by calculus methods the most economical speed and the least total cost of the whole voyage.