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The tickets to a charity concert will sell out if the price is $15 per ticket. it is estimated that for each $1 increase in ticket's price, 20 tickets will remain unsold. what ticket price will maximize the charity's profit, if there are total 500 seats in the concert hall?

Respuesta :

carlosego

Let's define variables:

x: number of times the ticket price increases ($ 1).

The income is given by:

I(x) = (15 + x)(500-20x)

We can rewrite this function in the following way:

I (x) = - 20x ^ 2 + 200x + 7500

We use the following equation to find the maximum:

max = (-b)/(2a)

where:

  • a=-20
  • b=200
  • c=7500

then, we have:

max = (-200)/(2(-20))

max = (200)/(40)

max=5

Thus, the ticket price that maximizes the benefit is:

15 + x = 15 + 5 = 20 $

Answer:

A ticket price that will maximize the charity's profit, if there are total 500 seats in the concert hall is:

$ 20

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