Regression equations are created by modeling data, such as the following:
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 values are given in thousands (i.e., the cost of making an individual e-reader will be $150 [0.15 × 1,000], with $28,000 [28 * 1,000] in constant charges). Answer the following questions based on the given regression equation:
Profit = (Cost 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 values are given in thousands (i.e., the cost of making an individual e-reader will be $150 [0.15 × 1,000], with $28,000 [28 * 1,000] in constant charges). Answer the following questions based on the given regression equation:
- 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)
- 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.)
- If the company does not sell a single e-reader, how much is lost ? Mathematically, what is this value called in the equation?
- If the company sells 5,000 e-readers, how much will the company make (or lose)?
- If profit must equal 100 thousand, how many e-readers will your company need to sell? (Round up to the nearest e-reader.)
- 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.)
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