Question

At a price of per ticket, a musical theater group can fill every seat in the theater, which has a capacity of . For every additional dollar charged, the number of people buying tickets decreases by . What ticket price maximizes revenue? Revenue is maximized when the price is

Answer 1

Answer:

The appropriate answer is "$12".

Step-by-step explanation:

As per the question,

Price per ticket,

= $4+k$

Number of people,

= $1800-90k$

Now,

The revenue (R) will be:

= $Price \ per \ ticket\times Number \ of \ people$

By putting the values, we get

= $(4+k) (1800-9k)$

= $-90k^2+1440k+7200$

or,

⇒ $R'=1440-180k=0$

⇒                     $180k=1440$

⇒                          $k=\frac{1440}{180}$

                               $=8$

hence,

The ticket price will be:

= $4+k$

= $4+8$

= $12$ ($)