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Optimizing for cost efficiency

  1. Oct 18, 2012 #1
    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. jcsd
  3. Oct 18, 2012 #2

    Ray Vickson

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    This cost per hour, not cost per mile.

    RGV
     
  4. Oct 18, 2012 #3
    I still don't understand. If you could give a more specific example that'd be great :P
     
  5. Oct 19, 2012 #4

    Ray Vickson

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    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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