Purchase Solution

Derivatives, Revenue Function, Maximizing Profit - Lemonade Stand

Not what you're looking for?

Ask Custom Question

Data:
regression equation: y= -100x + 250
regression coefficient: r= -1

X Y Predicted value
0.25 225 225
0.5 200 200
0.75 175 175
1 150 150
1.25 125 125
1.5 100 100
1.75 75 75
2 50 50
2.25 25 25
2.5 0 0

A. Create a function to determine how much revenue you will make at each price you charge. This is done by multiplying the price times your function. For example if your function is Cups Sold = 1000 - 100*Price, your revenue function would be Price*(1000 - 100*Price). For simplicity sake, you can write Price as "P".

B. What is the derivative of your revenue function?

C. Create a table (you can use Excel) with each of the columns:

1. The prices from the data above

2. The revenue you will make at each price

3. The value of the derivative at each price

D. At what price is your revenue maximized

E. What is the value of the derivative when you are charging more than the revenue maximizing price? How about when you are charging less? Based on this, how would you use the derivative to help you decide how much to charge for a cup of lemonade?

Purchase this Solution
Solution Summary

Derivatives, Revenue Function, Maximizing Profit are investigated for a lemonade stand. The solution is detailed and well presented.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Derivatives, Second Derivatives and Profit Function

    Derivatives, Second Derivatives and Profit Function are investigated for a lemonade stand. The solution is detailed and well presented.

  • Derivatives

    revenue function is R = pxq.

  • Regression : Function, Correlation Coefficient and Maximizing Profit - Lemonade Stand

    A Function, Correlation Coefficient and Maximizing Profit for a lemonade stand are investigated. The solution is detailed and well presented.

  • Profit-maximizing level of output

    386497 Profit-maximizing level of output With the total-revenue schedule of problem 1 (revised derivatives) and the total-cost schedule of problem 7 (cost function), show the profit-maximizing level of output? Problem history: 1.

  • Economies of scale

    321426 Explain Economies of scale for lemonade stand Compare: A young man has set up a lemonade stand on the corner of College Street and Air Park Boulevard. Temperatures in the area climb to 100 degrees during the summer.

  • Total Profit

    (This is obtained by taking the derivatives of the cost function with resp. to Q1 and Q2) The profit maximizing rule is MR = MC We now find the marginal revenues for each market Retail Revenue = (180 - 8Q1)Q1 = 180Q1 - 8Q1^2 marginal rev

  • Profit-maximizing amount, the optimal price

    profit = revenue - cost = price X quantity - cost at 1 - cost at 2 profit = [1000 - 5(Q + q)](Q + q) - 10,050 - 5Q^2 - 5,000 - 2q^2. Expanding the brackets leads to: profit = -10Q^2- 10Qq + 1000Q - 7q^2 + 1000q -15050.

  • Mathematics - Other

    224672 Suppose you own a lemonade stand. You have been experimenting with different prices per glass and have found that ... Suppose you own a lemonade stand.

  • Managerial Economics: Calculating Maximum Profit and Revenue

    372146 Managerial Economics: Calculating Maximum Profit and Revenue A monopolist's demand function is given by P = 80-3Q (with MR = 80-6Q). Its total cost function is TC = 20Q + 200 (with MC = 20).

View More Related Solutions