Optimizing for cost efficiency

  • Thread starter Painguy
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  • #1
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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?

Homework Equations





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?
 

Answers and Replies

  • #2
Ray Vickson
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This cost per hour, not cost per mile.

RGV
 
  • #3
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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
 
  • #4
Ray Vickson
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I still don't understand. If you could give a more specific example that'd be great :P

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

RGV
 

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