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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 3.1, Problem 77E

(a)

To determine

**To evaluate:** The function that models the revenue in terms of ticket price.

Expert Solution

The function that models the revenue in terms of ticket price is

**Given:**

A stadium that holds

**Calculation:**

Let the ticket price

The amount of ticket price is lowered

According to definition of revenue,

Increase in attendance is

Attendance in the recent game is

Total attendance is computed as follows.

From the equation (1) and (2),

The total revenue in terms of ticket price is,

Thus, the function that models the revenue in terms of ticket price is

(b)

To determine

**To evaluate:** The price that maximizes revenue from ticket sales.

Expert Solution

The price that maximizes revenue from ticket sales is

**Given:**

A stadium that holds

**Calculation:**

Let the ticket price is

The amount of ticket price is lowered is

According to definition of revenue,

Increase in attendance is

Attendance in the recent game is

Total attendance,

From the equation (1) and (2),

The total revenue in terms of ticket price,

From the equation (3),

The standard form of function,

The maximum or minimum value of the function occurs at,

If

If

From the equation (4) and (5),

Substitute

The value of

The function has maximum value

Thus, the price that maximizes revenue from ticket sales is

(c)

To determine

**To evaluate:** The maximum ticket price for which no revenue is generated.

Expert Solution

The maximum ticket price for which no revenue is generated is

**Given:**

A stadium that holds

**Calculation:**

Let the ticket price be

The amount of ticket price is lowered is

According to definition of revenue,

Increase in attendance is

Attendance in the recent game is

Total attendance,

From the equation (1) and (2),

The total revenue in terms of ticket price,

From the equation (3),

For the no revenue generated,

From the equation (4) and (5),

For the value of

For the maximum ticket price no revenue generated

The maximum ticket price for which no revenue generated is

Thus, the maximum ticket price for which no revenue is generated is