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Math Help - First year optimizing functions

  1. #1
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    First year optimizing functions

    I am attempting to do this question, but every time I look at it, I just get more confused. I have no idea how to even start. I'm especially confused about how to show the relationship between the values. Please help =/

    The cost of fuel (dollars/hour) to propel a ferry boat through water is proportional to the cube of the speed of the ferry boat. A certain ferry boat uses $100 of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the operational cost of running the ferry is $675 per hour. At what speed should the ferry boat cruise at to minimize the cost per mile traveled?
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    Re: First year optimizing functions

    Quote Originally Posted by jenniferz3 View Post
    I am attempting to do this question, but every time I look at it, I just get more confused. I have no idea how to even start. I'm especially confused about how to show the relationship between the values. Please help =/

    The cost of fuel (dollars/hour) to propel a ferry boat through water is proportional to the cube of the speed of the ferry boat. A certain ferry boat uses $100 of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the operational cost of running the ferry is $675 per hour. At what speed should the ferry boat cruise at to minimize the cost per mile traveled?
    F = kv^3 , where F is fuel cost in dollars/hr

    100 = k \cdot 10^3

    k = \frac{1}{10}

    total cost in dollars/hr = operational cost in dollars/hr + fuel cost in dollars/hr

    C = 675 + \frac{v^3}{10} , where C is total cost in dollars/hr

    finally, note that cost/mile = (cost/hr)/(miles/hr) ... optimize.
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    Re: First year optimizing functions

    Thank you so much! Worked out perfectly. D
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