A baseball team plays in a stadium that holds 48000 spectators. With the ticket price at $12 the averageattendance has been 21000. When the price dropped to $11, the average attendance rose to 24000. Assumethat attendance is linearly related to ticket price.What ticket price would maximize revenue? $

Name: A baseball team plays in a stadium that holds 48000 spectators. With
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Description: A baseball team plays in a stadium that holds 48000 spectators. With the ticket price at $12 the averageattendance has been 21000. When the price dropped to $11, the average attendance rose to 24000. Assumethat attendance is linearly related to tick

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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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A baseball team plays in a stadium that holds 48000 spectators. With the ticket price at $12 the average
attendance has been 21000. When the price dropped to $11, the average attendance rose to 24000. Assume
that attendance is linearly related to ticket price.
What ticket price would maximize revenue? $

Expert Solution

Step 1

Let the ticket price be $$ x$ and attendance is linear function of $x$ , say $P (x)$ .

When the ticket price at $12, average attendance is 21,000. Therefore, $P (12) = 21, 000$

When the ticket price is $11, average attendance is 24,000. Therefore, $P (11) = 24, 000$

Therefore, the slope of the line joining $(11, 24000)$ and $(12, 21000)$ is

$\begin{array}{rcl} m & = & \frac{21, 000 - 24, 000}{12 - 11} \\ = & - 3000 \end{array}$

Therefore, the equation of line joining these two points is

$P (x) = - 3000 x + 57000$ (i)

Eq.(i) represents the price function

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