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a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?



Answer :

An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

Given that;

The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,

Let 'T' be the number of times the price is decreased.

So, price;

     p = 38 – 5x

     x = (38 - p) / 5

And as per the given condition attendance;

a = 1000 + 50x

So, the Revenue is;

To develop an equation for revenue (r) as a function of p, the price of tickets;

R = p * a

R= p * (1000 + 50x)

But,  x = (38 - p) / 5

Then,

R = P * (1000 + 50(38 - p)/5)

  = p * (1000 + 380 - 10p)

  = p * (1380 – 10p)

  = 1380p - 10p²  → (I)

To get R(25) from (I);

R(25) = 1380(25) - 10(25)²

         = 34500 - 6250

         = 28250

Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

To learn more about revenue click here:

brainly.com/question/28558536

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