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Function and relation

  1. Jul 8, 2011 #1
    1. The problem statement, all variables and given/known data

    A manufacturer of bicycle parts, has a monthly fixed cost of $25 000, a production cost of $21.75 per unit and a selling price of $325 per unit.
    a) Cost function
    b) Revenue function
    c) Profit function
    d) Break-even point
    f) Cost when 150 units are produced.

    2. Relevant equations



    3. The attempt at a solution
    a) 25 000 (x) =$21.75 (x) + $325
     
  2. jcsd
  3. Jul 8, 2011 #2

    LCKurtz

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    You need to put in more steps to lessen your confusion. Call the cost, revenue and profit functions for x units C(x), R(x), and P(x). To answer the first three parts, finish these three equations:

    C(x) = ?
    R(x) = ?
    P(x) = ?

    with formulas in terms of x on the right side. Then we can talk.
     
  4. Jul 8, 2011 #3

    SteamKing

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    Your equation a) contains a couple of mistakes. The monthly fixed costs are constant: no matter how many bicycles are made, it takes $25000 to keep the plant open and ready for production. The $325 selling price for each bike is not charged to the company unless it decides to buy a bike at retail.

    You should also try to answer the other parts of the problem.
     
  5. Jul 8, 2011 #4
    i am not sure about the formulas
    C(x)= mx+b
    R(x) = mx
    P(x) = R(x) - C(x)
     
  6. Jul 8, 2011 #5

    LCKurtz

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    So what are m and b in this problem?
     
  7. Jul 8, 2011 #6
    m= selling price
    b= units

    C(x)= 325x+21.75
     
  8. Jul 8, 2011 #7

    LCKurtz

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    But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?
     
  9. Jul 8, 2011 #8
    it will cost $75
     
  10. Jul 8, 2011 #9
    ok so it would be
    C(x) = 325(x)+25 000
     
  11. Jul 8, 2011 #10

    LCKurtz

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    What about the $100 rent (or salaries or whatever for that day)?

    Once you answer that, what is the answer to build n widgets?

    And if I sell n of them for $150 each, how much revenue will I get?
     
  12. Jul 8, 2011 #11

    LCKurtz

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    NO! What does the $325 have to do with the cost???
     
  13. Jul 8, 2011 #12
    $325 is the selling price
    i dont know the formula, i think once i have the formula i will be able to do it
     
  14. Jul 8, 2011 #13

    LCKurtz

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    I am trying to help you understand how to figure out the formula. It would help if you would answer the widget questions I have posted above. Please don't edit some previous post; just reply to this one.
     
  15. Jul 8, 2011 #14
    it will cost $175 to build n widgets

    And if u sell n of them for $150 each, would get $450
     
  16. Jul 8, 2011 #15

    LCKurtz

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    Those are the answers for 3 widgets. What are the answers for n?
     
  17. Jul 8, 2011 #16
    would n=3
     
  18. Jul 8, 2011 #17

    LCKurtz

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    You need to use n in the formulas instead of 3 if that's what you are asking. What do you get for both questions?
     
  19. Jul 8, 2011 #18
    that's the thing, i dont know the formula
     
  20. Jul 8, 2011 #19

    LCKurtz

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    But you do know the formula if you just think about it. You answered both my questions for 3 widgets. You did a mental calculation to get those answers. You did a calculation using the number 3. Can you do the same calculation for 4 widgets? 5? 6?

    Just describe the calculation you did but use n instead of a specific number. I know you can do it.
     
  21. Jul 8, 2011 #20
    is it
    n= 25(n) + 100
     
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