Marginal Revenue-derivatives

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In summary, the conversation discusses using derivatives to find the answer to a problem related to bus fares and revenue. The formula for total revenue per trip is given, and the conversation goes on to talk about finding the number of passengers and corresponding fare that would result in zero marginal revenue. The correct method is to use derivatives and set it equal to zero, but there may have been an arithmetic error in the calculation.
  • #1
salemchic05
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We're in the derivatives chapter, so we assume finding the answer to this requires the use of a derivative, but we are completely lost.

A bus will hold 60 people. The fare charged (p dollars) is related to the number x of people who use the bus by the formula p=[3-(x/40)]^2.

(a) Write a formula for the total revenue per trip received by the bus company. ***Here we got the answer-R(x)=[3-(x/40)]^2(x)

(b) What number of people per trip will make the marginal revenue equal to zero? What is the corresponding fare? ***this is where we thought we should use the derivative and set it equal to zero, but our answer is amillion miles off from the answer given in the book. The answer we are given is 40 and a $4 fare. :bugeye:
 
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  • #2
Your method is correct and gives the right answer. You must have made an arithmetic error. Check your work.
 
  • #3
salemchic05 said:
(a) Write a formula for the total revenue per trip received by the bus company. ***Here we got the answer-R(x)=[3-(x/40)]^2(x)
Would it not be:

Revenue = no. passengers x fare per passenger

[tex]R = x(3-x/40)^2 = 9x -6x^2/40 + x^3/1600[/tex]

(b) What number of people per trip will make the marginal revenue equal to zero? What is the corresponding fare? ***this is where we thought we should use the derivative and set it equal to zero, but our answer is amillion miles off from the answer given in the book. The answer we are given is 40 and a $4 fare.
You are trying to find the point where the change in revenue per change in unit passenger = 0. How does this relate to the derivative of Revenue with respect to x? For what values of x does the derivative = 0?

AM
 

What is marginal revenue?

Marginal revenue is the additional revenue earned by selling one additional unit of a product. It is calculated by dividing the change in total revenue by the change in quantity sold.

How is marginal revenue related to derivatives?

Marginal revenue is the derivative of the total revenue function with respect to quantity. This means that it represents the rate of change of revenue with respect to quantity.

Why is understanding marginal revenue important?

Understanding marginal revenue is important because it helps businesses make decisions about pricing and production levels. It can also provide insights into consumer behavior and market demand.

What is the relationship between marginal revenue and marginal cost?

The relationship between marginal revenue and marginal cost is important in determining the profit-maximizing quantity for a business. When marginal revenue is greater than marginal cost, a business should increase production, and when marginal revenue is less than marginal cost, a business should decrease production.

How does marginal revenue impact a company's revenue and profit?

Marginal revenue has a direct impact on a company's revenue and profit. When marginal revenue is positive, it adds to the company's total revenue and increases profit. When marginal revenue is negative, it decreases the company's total revenue and decreases profit.

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