# Optimizing for cost efficiency

1. Oct 18, 2012

### Painguy

1. The problem statement, all variables and given/known data
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?
2. Relevant equations

3. 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?

2. Oct 18, 2012

### Ray Vickson

This cost per hour, not cost per mile.

RGV

3. Oct 18, 2012

### Painguy

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

4. Oct 19, 2012

### Ray Vickson

No. That would be doing your homework for you, which is forbidden. I have already given a perfectly adequate hint.

RGV