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Bread-Even Analysis

  1. Jan 16, 2008 #1
    Hey guys, here's the problem and what I've got so far.

    A contractor purchases a piece of equipment for $36500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour.

    (a) Write an equation for the cost C of operating this equipment for t hours
    (b) Write an equation for the revenue R derived from t hours of use
    (c) Find the break-even point for this equipment by finding the time at which R = C

    What I've got:

    (a)
    [tex] C = 22.75(t)+36500[/tex]

    (b)
    [tex]R=30(t)+36500[/tex]

    (c - worked out)
    [tex]0 = -7.25(t) + 36500[/tex]
    [tex]5034.48 = t[/tex]
    does this look right?
     
  2. jcsd
  3. Jan 17, 2008 #2

    HallsofIvy

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    Yes, that's good. For a moment I didn't reconize that the "22.75" includes both fuel and maintenance and the operator!

    No! The cost of the equipment is not Revenue. R= 30 t. Was that a typo? You don't use it in C.

    I would recommend showing a little more work. "Break even" occurs when revenue= cost: 30 t= 22.75 t+ 36500. Subtracting 22.75 t from both sides,
    7.25 t= 36500 so t= 36500/7.25= 5034.48.

    The break even point will occur after 5034.48 hours of use. The "units", hours, is an important part of the answer: not just "503448"!

    Showing, and explaining, every detail, as well as specifically answering the question with a full sentence will shock and amaze your teacher!


    (I did wonder what "Bread Even Analysis" was. Determining whether you have enough sandwiches to go around?)
     
    Last edited: Jan 17, 2008
  4. Jan 17, 2008 #3
    ha! I tried to fix it but couldn't

    So the answer should have been [tex]R=30t[/tex] instead? Or did I miss something you said..


    On the last part, I did get the right answer but I just need to show more work, correct?
     
  5. Jan 18, 2008 #4

    HallsofIvy

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    Yes, that was what I said.


    Yes. Of course, your teacher might not require that, but it is always good practice- if nothing else, it helps you organize your thoughts.
     
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