non-linear regression

Derivatives

General Guidelines

1.       The questions and all the required data are included in this template.

2.       Word-process your case assignment within this template. Do not create a new file.

3.       Do not change the header or footer. They contain course number, term, name of case and page number, which are all required.

4.       Use 12 point regular font and 1.5 line spacing. Do not use italics for your write-up.

5.       Use Equation Editor (Insert/ Object/ Microsoft Equation) to word-process the formulas, if required for the case.

6.       Use Excel for graphs and the drawing tool in Word for diagrams, if required for the case.

7.       Create a single Word document by pasting all your Excel work into this Word document.

8.       Use the rules of rounding correctly at all steps including the final answers. Note: 0.12344 is rounded to 0.1234 and 0.12345 is rounded to 0.1235.

9.       Do minimum rounding at intermediate steps (use at least four significant digits). Round off the final answers appropriately. Note: 0.0042 is only two significant digits as leading zeros are not considered significant. 0.4200 is four significant digits as trailing zeros are considered significant.

Question #1:

In the file Week7data.xls is a tab labeled “Price vs. Number of Items Sold”.  The first column is the price charged for a point of purchase dog toy in several different markets, while the second column is the number items sold of that item.  Plot the data with items sold as the y-variable and determine the quadratic fit to the data.  Insert the plot below and write out the quadratic equation allowing you to predict sales as a function of the price charged.

Question #2:

What price would you charge to maximize items sold? (Use the quadratic fit you determined above.)

Question #3:

Write out a quadratic equation which predicts revenue given the price charged.  (Use the same procedure as in Question #1.)

 

Question #4:

What price would you charge to maximize revenue? (Use the quadratic equation from Question #3.)

 

Question #5:

The cost of manufacturing one of the toys is given by the following equation:

Use this function to determine the cost of making the toys in each market for which you have data.  Use this cost data to determine the profit you make for each market.  Finally, use the profit data to determine what price you should set to maximize profit. (Use the same procedure as in Question #1 and Question #2).

 

Question #6:

 

Point out one area where the set up of this homework is unrealistic.