Concept explainers
(a)
To find: The revenue of the theatre as the function of the ticket price.
(a)
Answer to Problem 83E
The expression for the revenue function is
Explanation of Solution
Given:
The capacity of the theatre has the sitting capacity of
Calculation:
Consider the revenue function of the attendance as the function of the ticket prize is,
Then, the revenue when the ticket prize is of
So, the equation for the revenue is,
Then, the revenue when the ticket prize is of
So, the equation for the revenue is,
Then, the revenue when the ticket prize is of
So, the equation for the revenue is,
From above, from equation (I) and equation (II), the values are,
The expression for the revenue function is,
(b)
To find: The ticket price for the maximum revenue and the maximum revenue,
(b)
Answer to Problem 83E
The ticket price for maximum revenue is
Explanation of Solution
The value of the ticket price for the maximum revenue is,
Then,
The revenue for the ticket price of
The ticket price for maximum revenue is
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
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