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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 :

Cricetus

Answer:

The appropriate answer is "$12".

Step-by-step explanation:

As per the question,

Price per ticket,

= [tex]4+k[/tex]

Number of people,

= [tex]1800-90k[/tex]

Now,

The revenue (R) will be:

= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]

By putting the values, we get

= [tex](4+k) (1800-9k)[/tex]

= [tex]-90k^2+1440k+7200[/tex]

or,

⇒ [tex]R'=1440-180k=0[/tex]

⇒                     [tex]180k=1440[/tex]

⇒                          [tex]k=\frac{1440}{180}[/tex]

                               [tex]=8[/tex]

hence,

The ticket price will be:

= [tex]4+k[/tex]

= [tex]4+8[/tex]

= [tex]12[/tex] ($)

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