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# Mathematics - Other

Suppose you own a lemonade stand. You have been experimenting with different prices per glass and have found that you sell the following cups per day depending on the price you charge:

Price Cups Sold
0.25 225
0.5 200
0.75 175
1 150
1.25 125
1.5 100
1.75 75
2 50
2.25 25
2.5 0

Now that your experiment is over you wish to find a function to tell you how many cups you will sell as a function of the price. Since the consultant from Price Waterhouse charges \$500 per hour to estimate this function for you, you have decided instead to estimate the function yourself.
Luckily, there is a method using calculus that helps you estimate functions from data. This is called the method of least squares, also known as regression. Also, lucky for you there are web pages that do the calculations for you. Here is one such page:
Simple Regression Page http://people.hofstra.edu/faculty/Stefan_Waner/newgraph/regressionframes.html

To calculate your function, type in the prices in the column marked "X" and type in the number of cups sold in the column market "Y". Then hit the button marked "Y= mX + b".
The Answers Are:
The Regression Equation
Y= -100x + 250
Regression Coefficient
r = -1

After you have your answer, report your results in an executive summary that includes,
A. Your function, and specify what the slope and intercept of your function is.
B. What this function tells you about the relationship between the price and the number of cups sold.
C. How you plan on using this function to help you maximize the profits of your lemonade stand.

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.

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