Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please answer ALL of the questions fully!
You get a job as the manager of a popular ice cream store in your hometown. One of your first concerns is determining how much ice cream you should stock to meet the demands of your customers. You suspect that the number of customers buying ice cream probably depends on several factors.
- What factors do you think might affect the number of customers buying ice cream?
- As the store manager, how could you tell if these factors do have an effect?
- How would you collect data for these factors? Make sure you include possible difficulties which you may encounter.
- How could you generalize or predict from your data? How much faith do you have in your predictions? Explain.
In looking through company files, you discover that the former manager collected considerable data. Last summer, a typical week produced the following data:
|
Day |
Temperature (degrees Fahrenheit) |
Number of Transactions |
Gross Receipts (in dollars) |
|
Monday |
78 |
238 |
3014 |
|
Tuesday |
73 |
194 |
2842 |
|
Wednesday |
70 |
172 |
2141 |
|
Thursday |
75 |
185 |
2235 |
|
Friday |
83 |
270 |
4505 |
|
Saturday |
89 |
320 |
5021 |
|
Sunday |
94 |
280 |
4442 |
On the graph below, the temperature is graphed on the x axis and the number of transactions is graphed on the y axis.
Investigate the relationship between the temperature and the gross receipts. On the grid below, graph temperature on the x axis (input) versus gross receipts on the y axis. (output)
Investigate the relationship between number of transactions (input) and gross receipts (output) by graphing the ordered pairs.
- Based on your data, predict the number of transactions if the temperature reaches 98 °. Explain how you made this prediction and how accurate you think it is.
- Based on your data, predict the gross receipts if the temperature is 80°. Explain how you made this prediction and how accurate you think it is.
- Based on your data, predict the number of transactions if the temperature falls to 65 °. Explain how you made this prediction and how accurate you think it is.
- As the number of transactions increases, what can you say about the gross receipts? Explain how you arrived at your conclusion.
- Describe the other functions which last year's manager neglected to consider.
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