(a) time = distance/speed, so a trip of 1000km takes 1000/v hours. So, the cost is
c(v) = (1000/v)(160 + 1/100v^3)
(b) Now just find minimum cost where dc/dv = 0
dc/dv = 20(v^3-8000)/v^2
so minimum cost when v=20
(c) Since min occurs at v=20, if top speed is 16, then minimum occurs at 16
The cost of running a ship at a constant speed of v km/h is 160 + 1/100*v^3 dollars per hour.
a)Find the cost of a journey of 1000km at a speed of v km/h.
b)Find the most economical speed for the journey, and the minimum cost.
c)If the ship were to have maximum speed of 16 km/h find what the minimum cost would be.
1 answer
1 answer