Chapter 9.9, Problem 4BGP

To determine

To calculate the revenue of the theater.

Answer to Problem 4BGP

Revenue of the theater per show

  $R(3)=\$4387.5$

Explanation of Solution

Given information:

Current price of ticket is $18

Number of tickets sell is 250

25 more ticket sell when for every $1.5 decrease in the price

Manager decided to sell tickets at price $13.5

Calculation:

Let x is number of $1.5 decrease in the price

Current price of ticket $=\$18$

Then, tickets sell $=250$

When x number of $1.5 decrease price of tickets

Then price the function of price,

  $p(x)=18-1.5x$

Then number of tickets sold,

  $T(x)=250+25x$

Then revenue of the theater per show,

  $R(x)=P(x)\times T(x)$

When maneger decided to sell tickets at price $13.5

Then number of decrease in $1.5, $x=3$

Revenue

  $R(x)=P(x)\times T(x)$

Sunstituting value of function of price and number of tickets sold

  $R(x)=(18-1.5x)(250-25x)$

Then

On putting $x=3$ in above

  $R(3)=(18-1.5(3))(250+25(3))$

On solving,

  $R(3)=(13.50)(250+75)$

On solving,

  $R(3)=(13.50)(325)$

On solving,

  $R(3)=\$4387.5$