The table gives the price, in dollars, of a round-trip ticket from Denver to Chicago on a certain airline and the corresponding monthly profit, in millions of dollars, for that airline. Profit from the Sale of Round-Trip Tickets Profit Ticket Price (dollars) (million dollars) 200 3.38 250 3.90 300 4.23 350 4.38 400 4.34 450 4.12 (a) Explain why a quadratic model is more appropriate for the data than a log or exponential model. O The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not possess maximum points but quadratic functions do. O The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. O The data indicates minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do not possess minimum points, but quadratic functions do. O The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. (b) Find a quadratic model for the data. (Round all numerical values to six decimal places.) P(x) = million dollars (c) Why doesn't the airline profit increase as the ticket price increases? O The airline has to provide more amenities for passengers to justify the price increase. O More taxes must be paid on the increased revenue. O As ticket prices increase, fewer tickets will be sold at the increased price leading to a decline in profit. O Crew members have their pay increased when ticket prices go up. (d) Report the ticket price (to the nearest dollar) at which the airline will begin to post a negative profit (that is, a net loss). dollars
The table gives the price, in dollars, of a round-trip ticket from Denver to Chicago on a certain airline and the corresponding monthly profit, in millions of dollars, for that airline. Profit from the Sale of Round-Trip Tickets Profit Ticket Price (dollars) (million dollars) 200 3.38 250 3.90 300 4.23 350 4.38 400 4.34 450 4.12 (a) Explain why a quadratic model is more appropriate for the data than a log or exponential model. O The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not possess maximum points but quadratic functions do. O The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. O The data indicates minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do not possess minimum points, but quadratic functions do. O The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease. (b) Find a quadratic model for the data. (Round all numerical values to six decimal places.) P(x) = million dollars (c) Why doesn't the airline profit increase as the ticket price increases? O The airline has to provide more amenities for passengers to justify the price increase. O More taxes must be paid on the increased revenue. O As ticket prices increase, fewer tickets will be sold at the increased price leading to a decline in profit. O Crew members have their pay increased when ticket prices go up. (d) Report the ticket price (to the nearest dollar) at which the airline will begin to post a negative profit (that is, a net loss). dollars
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Analysis of Airline Ticket Pricing and Profit
The table below illustrates the relationship between the price of a round-trip ticket from Denver to Chicago and the corresponding monthly profit for an airline, presented in millions of dollars.
#### Profit from the Sale of Round-Trip Tickets
| Ticket Price (dollars) | Profit (million dollars) |
|------------------------|--------------------------|
| 200 | 3.38 |
| 250 | 3.90 |
| 300 | 4.23 |
| 350 | 4.38 |
| 400 | 4.34 |
| 450 | 4.12 |
### Questions and Analysis
#### (a) Model Selection
**Explain why a quadratic model is more appropriate for the data than a logarithmic or exponential model.**
- The data indicates a maximum and changes from increasing to decreasing at the peak point. Logarithmic and exponential functions typically do not exhibit maximum points, whereas quadratic functions do.
Options:
- ○ The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease.
- ○ The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do not possess minimum points, but quadratic functions do.
- ● The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not possess maximum points but quadratic functions do.
- ○ The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease.
#### (b) Quadratic Model
**Find a quadratic model for the data. (Round all numerical values to six decimal places.)**
\[ P(x) = \_\_\_\_\_\_\_\_\_ \text{ million dollars} \]
(Placeholder for the actual quadratic model equation)
#### (c) Factors Affecting Profit
**Why doesn’t the airline profit increase as the ticket price increases?**
- Option:
- ○ The airline has to provide more amenities for passengers to justify the price increase.
- ○ More taxes must be paid on the increased revenue.
- ● As ticket prices increase, fewer tickets will be sold at the increased price leading to a decline in profit.
- ○ Crew members have their pay increased when ticket prices go up](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1446b12-d593-46d1-b995-c0d8e06662e6%2Fb8c87df1-595e-43c1-b626-afe9a343cbd2%2F64ltnzo_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Airline Ticket Pricing and Profit
The table below illustrates the relationship between the price of a round-trip ticket from Denver to Chicago and the corresponding monthly profit for an airline, presented in millions of dollars.
#### Profit from the Sale of Round-Trip Tickets
| Ticket Price (dollars) | Profit (million dollars) |
|------------------------|--------------------------|
| 200 | 3.38 |
| 250 | 3.90 |
| 300 | 4.23 |
| 350 | 4.38 |
| 400 | 4.34 |
| 450 | 4.12 |
### Questions and Analysis
#### (a) Model Selection
**Explain why a quadratic model is more appropriate for the data than a logarithmic or exponential model.**
- The data indicates a maximum and changes from increasing to decreasing at the peak point. Logarithmic and exponential functions typically do not exhibit maximum points, whereas quadratic functions do.
Options:
- ○ The data indicates the graph is only increasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease.
- ○ The data indicates a minimum point and changes from decreasing to increasing at that point. Logarithmic and exponential functions do not possess minimum points, but quadratic functions do.
- ● The data indicates a maximum and changes from increasing to decreasing at the point. Logarithmic and exponential functions do not possess maximum points but quadratic functions do.
- ○ The data indicates the graph is only decreasing. Logarithmic and exponential functions both increase and decrease while quadratic functions either increase or decrease.
#### (b) Quadratic Model
**Find a quadratic model for the data. (Round all numerical values to six decimal places.)**
\[ P(x) = \_\_\_\_\_\_\_\_\_ \text{ million dollars} \]
(Placeholder for the actual quadratic model equation)
#### (c) Factors Affecting Profit
**Why doesn’t the airline profit increase as the ticket price increases?**
- Option:
- ○ The airline has to provide more amenities for passengers to justify the price increase.
- ○ More taxes must be paid on the increased revenue.
- ● As ticket prices increase, fewer tickets will be sold at the increased price leading to a decline in profit.
- ○ Crew members have their pay increased when ticket prices go up
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