A concert hall has 12,000 seats and two categories of ticket prices, S32 and $42. Assume that all seats in each category can be sold. Concert 2 12,000 $403,000 3 12,000 $415,000 Tickets sold 12,000 S455,000 Return required

Advanced Engineering Mathematics
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ISBN:9780470458365
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A concert hall has 12,000 seats and two categories of ticket​ prices, $32 and ​$42. Assume that all seats in each category can be sold.

a. How many tickets of each category should be sold to bring in each of the returns indicated in the table?

b. Is it possible to bring in a return of 750,000 when all the seats are sold?

c. Describe all possible returns

 

### Concert Hall Revenue Analysis

A concert hall has a total of 12,000 seats and offers two categories of ticket prices: $32 and $42. The assumption is made that all seats in each category will be sold.

#### Concert Revenue Data

The table below displays the number of tickets sold and the corresponding returns required for three different concerts:

| Concert | Tickets Sold | Return Required |
|---------|---------------|-----------------|
| 1       | 12,000        | $455,000        |
| 2       | 12,000        | $403,000        |
| 3       | 12,000        | $415,000        |

### Analysis

All three concerts sold out, with 12,000 tickets purchased for each event. Despite the consistent number of tickets sold, the returns required for each concert varied:

- **Concert 1:** The return required was the highest at $455,000.
- **Concert 2:** This concert required the lowest return of $403,000.
- **Concert 3:** The required return for this concert was $415,000.

This data can be used to analyze the pricing strategy and operational costs associated with different concerts in the same venue.
Transcribed Image Text:### Concert Hall Revenue Analysis A concert hall has a total of 12,000 seats and offers two categories of ticket prices: $32 and $42. The assumption is made that all seats in each category will be sold. #### Concert Revenue Data The table below displays the number of tickets sold and the corresponding returns required for three different concerts: | Concert | Tickets Sold | Return Required | |---------|---------------|-----------------| | 1 | 12,000 | $455,000 | | 2 | 12,000 | $403,000 | | 3 | 12,000 | $415,000 | ### Analysis All three concerts sold out, with 12,000 tickets purchased for each event. Despite the consistent number of tickets sold, the returns required for each concert varied: - **Concert 1:** The return required was the highest at $455,000. - **Concert 2:** This concert required the lowest return of $403,000. - **Concert 3:** The required return for this concert was $415,000. This data can be used to analyze the pricing strategy and operational costs associated with different concerts in the same venue.
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