PART II:  Applied Exercises (90 points)

PART II:  Applied Exercises (90 points)

Task Background: Break-even analysis is a very powerful tool for making decisions. For example, the number of items that your company produces may not be enough to make a profit.  Break-even analysis  is often used in businesses to make predictions for the sales of goods and services. Graphs of break-even equations help to make these predictions by providing a visual relationship between two variables. 

Assignment

Windows Based Computers: Download the graphing program from www.padowan.dk/graph. Instructions can be found here.

Apple (Mac) Based Computers: Download the graphing program from http://www.geogebra.org/cms/.

(NOTE: You are free to use Excel as well if preferred).

Scenario: Break-even equations are created by modeling data, such as the following:

Profit = (Profit Per Item × Number of Items) – Constant Charges

In this equation, constant charges may be rent, salaries, or other fixed costs. This includes anything that you have to pay for periodically as a business owner. This value is negative because this cost must be paid each period and must be paid whether you make a sale or not.

Your company may wish to release a new e-reader device. Based on data collected from various sources, your company has come up with the following regression equation for the profit of the new e-reader:

Profit = $0.15 × number of e-readers sold – $28

Or, assuming x = the number of e-readers sold, this would be the same regression equation:

Profit = 0.15x – 28

  

In this case, the monetary values are given in thousands. This means that you will have to multiply them by 1000 to get the actual amount. For example, to find the profit or loss on a single e-reader, replace 
x with 1 as in the following.

Profit = 0.15(1) – 28 = -27.85, which indicates a loss of $27,850  Answer the following questions based on the given regression equation:

1. Using the graphing program that you downloaded, graph the profit equation. Discuss the meaning of the x- and y-axis values on the graph. (Hint: Be sure to label the axis) 
2. Discuss the meaning of the slope of the equation that you have just graphed.  How is it related to the profit of each e-reader?
3. Based on the results of the graph and the profit equation provided, discuss the relationship between profits and number of e-readers produced. (Hint: Consider the slope and y-intercept.)
4. If the company does not sell a single e-reader, how much is lost ? Mathematically, what is this value called in the equation?
5. If the company sells 5,000 e-readers, how much will the company make (or lose)?
6. If profit must equal 100 thousand, how many e-readers will your company need to sell? (Round up to the nearest e-reader.)
7. If your company is hoping to break even, how many e-readers will need to be sold to accomplish this? (Round up to the nearest e-reader.) Hint: At the break-even point, there is neither a profit nor a loss.

Please submit your assignment.