Finding the derivative of a revenue function

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Homework Help Overview

The discussion revolves around finding the derivative of a revenue function, specifically the relationship between revenue, price, and quantity sold. The revenue function is given as r = 8x, with x representing the number of units sold, and a demand function q = -1/4p + 10000, where q is the quantity sold at price p. Participants are exploring how to derive dr/dp based on these functions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of the product rule and chain rule in differentiating the revenue function. There is uncertainty about how to correctly apply these rules to the equation r = p * f(p). Some participants express confusion regarding the implications of the revenue function and demand function on the derivative.

Discussion Status

There is ongoing exploration of the derivative with various approaches being suggested, including the use of the product and chain rules. Some participants question the formulation of the problem and its logical consistency, indicating a lack of consensus on the correct interpretation of the revenue function and its relationship to price and quantity.

Contextual Notes

Participants note potential issues with the problem statement, particularly regarding the relationship between revenue and price when using the given functions. There is a suggestion that if revenue is constant, the derivative may not vary, leading to further questioning of the problem's setup.

tech_chic
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Homework Statement


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?

Homework Equations


r=pq

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.
 
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tech_chic said:

Homework Statement


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?

Homework Equations


r=pq

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.

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?
 
I'm thinking I would use the product rule. but I'm still confused on the equation 'r = p * f (p).
 
tech_chic said:
I'm thinking I would use the product rule. but I'm still confused on the equation 'r = p * f (p).

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?
 
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.
 
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
 
tech_chic said:
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.

Start with applying the chain rule to the equation r = p * f(p). Don't worry about substituting for f(p) at first.
 
tech_chic said:

Homework Statement


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?

Homework Equations


r=pq

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.

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.
 

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