Results 1 to 2 of 2

Math Help - Optimization, Minimization Calculus Problem--I'm Stuck!

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    USA
    Posts
    1

    Optimization, Minimization Calculus Problem--I'm Stuck!

    The problem I'm working on is...

    A truck gets
    500/x
    miles per gallon (mpg) when driven at a constant speed of x mph, where 40 ≤ x ≤ 80.
    If the price of fuel is $2.80/gal and the driver is paid $20/hr, at what speed is it most economical for the trucker to drive?

    I have been searching for similar problems in my text book and class notes but am unable to find one. I'd greatly appreciate any help or similar examples!

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2013
    From
    Northwestern East Coast
    Posts
    1

    Re: Optimization, Minimization Calculus Problem--I'm Stuck!

    The trick of it is to find what you want to optimize. In this case it would be miles per dollar.

    You are given miles/gallon, dollars/gallon, miles/hour, and dollars/hour.

    Your equation will be made up of two pieces, your fuel miles/dollar and your driver's miles/dollar. The sum of these will create your total miles/dollar.

    Spoiler:
    (miles/gallon) / (dollars/gallon) = fuel miles/dollar
    (500/x) / (2.8) = 500/(2.8x)

    miles/hour / dollars/hour = driver miles/dollar
    x / 20 = x/20

    fuel miles/dollar + driver miles/dollar = total miles/dollar
    500/(2.8x) + x/20 = f(x)


    Once your equation is set up it is straight forward optimization.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization Problem Need Almost Done Stuck
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 13th 2013, 11:10 AM
  2. Stuck on simple calculus problem...
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 27th 2010, 06:19 PM
  3. Replies: 4
    Last Post: June 3rd 2009, 03:29 PM
  4. Optimization: Minimization
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 11th 2007, 12:06 PM
  5. Optimization problem, stuck
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 11th 2006, 12:15 AM

Search Tags


/mathhelpforum @mathhelpforum