# Optimizing for cost efficiency

## Homework Statement

The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed v. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is$3125 per hour.
(a) Find the proportionality constant for the cost of the fuel per hour.

(b) Express the cost per mile in terms of v only.

(c) At what speed should the boat travel so as to minimize the cost per mile traveled?

## The Attempt at a Solution

a) C=kv^3

100=k1000
k=.1

b)C(v)=.1kv^3 + 3125

This is where i get stuck because apparently this is wrong?

Ray Vickson
Homework Helper
Dearly Missed
This cost per hour, not cost per mile.

RGV

This cost per hour, not cost per mile.

RGV

I still don't understand. If you could give a more specific example that'd be great :P

Ray Vickson