Concert ticket prices are $18 for a screening with 500 attendees. for each $1 increase in ticket price, attendance decreased by 5 people. what should the ticket price be to maximize revenue?

$59

Step-by-step explanation:

Let the revenue will be maximum when $ x is increased in the ticket price.

So, the final ticket price is $(18 + x) and attendance in the concert will be (500 - 5x)

So, revenue R = (18 + x) (500 - 5x) = 9000 + 410x - 5x².......... (1)

Condition for R to be maximum is

So, differentiating equation (1) with respect to x on both sides

⇒ x = 41

So, the ticket price for maximum revenue is $(18 + 41) = $59 (Answer)

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation: