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.