3. A small theater has a seating capacity of 2000. When the ticket price is $20, attendance is 1500. After a price decrease of $2, however, the attendance increased to 1700. Assuming that the demand function is linear, what ticket price will maximize the revenue? 8 Pts.
3. A small theater has a seating capacity of 2000. When the ticket price is $20, attendance is 1500. After a price decrease of $2, however, the attendance increased to 1700. Assuming that the demand function is linear, what ticket price will maximize the revenue? 8 Pts.
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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Transcribed Image Text:**Problem Statement:**
A small theater has a seating capacity of 2000. When the ticket price is $20, attendance is 1500. After a price decrease of $2, however, the attendance increased to 1700. Assuming that the demand function is linear, what ticket price will maximize the revenue?
**Explanation:**
1. **Initial Condition:**
- Ticket Price: $20
- Attendance: 1500
2. **After Price Decrease:**
- New Ticket Price: $18 ($20 - $2)
- New Attendance: 1700
The objective is to find the ticket price that maximizes revenue, considering the linear demand function.
**Points: 8**
This problem requires understanding of demand functions and maximizing revenue using linear relationships. It involves calculating the revenue for different ticket prices and determining the optimal price point.
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