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Homework Help: Related Rates Cell Phone Problem

  1. Nov 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The average cost per item, C, in dollars, of manufacturing a quantity q of cell phones is given by the following equation, where a and b are positive constants.
    C = a/q + b

    (a) Find the rate of change of C as q increases. Include units.

    I already found this, it's: -a/q^2

    ***(b) If production increases at a rate of 130 cell phones per week, how fast is the average cost changing? Include units.

    B is the one I need help with.

    3. The attempt at a solution

    So far for part "b", I've figured out that dq/dt is 130, so I differentiated C = a/q + b implicitly
    and got dC/dt = -a/q^2 (dq/dt) + b. I plugged in 130 for dq/dt and got

    dC/dt = -130a/q^2 + b

    I have no idea where to go from here.

    Any help would be greatly appreciated!
  2. jcsd
  3. Nov 11, 2009 #2


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    Hi alyplayford! :smile:
    No, b is constant. :wink:

    Now eliminate q from the RHS to get a differential equation in C. :smile:
  4. Nov 11, 2009 #3
    What is RHS? And do I need to solve for q? How do I do that?
  5. Nov 11, 2009 #4


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    Right-hand side! :wink:

    And C = a/q + b.
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