math
posted by sharon .
Scenario: Regression equations are created by modeling data, such as the following:
Sales = (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 ereader device. Based on data collected from various sources, your company has come up with the following regression equation for the sales of the new ereader:
Sales = $0.15 × number of ereaders sold – $28
Or, assuming x = the number of ereaders sold, this would be the same regression equation:
Sales = 0.15x – 28
In this case, the values are given in thousands (i.e., the cost of making an individual ereader 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:
1. Discuss the meaning of the x and yaxis values on the graph. (Hint: Label the axis with the Text tool in the graphing program.)
2.Based on the results of the graph and the sales equation provided, discuss the relationship between sales and number of ereaders produced. (Hint: Consider the slope and yintercept.)
3.If the company does not sell a single ereader, how much is lost in sales? Mathematically, what is this value called in the equation?
4.If the company sells 5,000 ereaders, how much will the company make (or lose) in sales?
5.If sales must equal 100 thousand, how many ereaders will your company need to sell? (Round up to the nearest ereader.)
6.If your company is hoping to break even, how many ereaders will need to be sold to accomplish this? (Round up to the nearest ereader.)
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