1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the derivative of a revenue function

  1. Oct 30, 2014 #1
    1. The problem statement, all variables and given/known data
    The revenue function for a product is r = 8x where r is in dollars and x is the number of units sold. the demand function is q = -1/4p + 10000 where q units can be sold when selling price is p. what is dr/dp?

    2. Relevant equations
    r=pq

    3. The attempt at a solution
    I substituted the values into r=pq.

    8x= -1/4p^2 + 10000p

    i'm not sure which rule to use from here to find the derivative or if i overcomplicated the question.
     
  2. jcsd
  3. Oct 30, 2014 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    You got slightly off track.

    r = pq and q is a function of p. In essence, you have r = p * f(p). How would you find dr/dp now?
     
  4. Oct 30, 2014 #3
    I'm thinking I would use the product rule. but I'm still confused on the equation 'r = p * f (p).
     
  5. Oct 30, 2014 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    It's not clear why you are still confused.

    The product rule is OK, but is that rule all that you need to find dr/dp?
     
  6. Oct 30, 2014 #5
    oh yeah the chain rule as well. and I'm still partially confused because I'm not sure how to use the rules on the equation.
     
  7. Oct 30, 2014 #6

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can someone explain why "r = 8x where r is in dollars and x is the number of units sold" and "there are 10000 - p/4 units sold if the price is p" does not lead to r = 8p ?

    And hence dr/dp = -2 and revenue is maximum ($ 80000) if you give the product away for free ?

    It doesn't sound logical, so either I am misunderstanding, or I am misinformed in the problem formulation
     
  8. Oct 30, 2014 #7

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Start with applying the chain rule to the equation r = p * f(p). Don't worry about substituting for f(p) at first.
     
  9. Oct 30, 2014 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    There is something seriously wrong with your problem statement. If, in fact, the revenue really is r = 8x (x = number sold), then the price must = 8 (=the coefficient of the number sold in the expression for r), and you have x = 10000(8) - (1/4)8^2 = 79984 and r = 8x = 639872. Nothing is varying, so the derivative = 0.

    On the other hand, if you want the derivative of r = p*q(p) at p = 8, that is an entirely different question. The equation you wrote (8x = -1/4 p^2 + 10000 p) makes no sense.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding the derivative of a revenue function
Loading...