Question

How do I answer this.
The cost of a ticket to a hockey arena seating 8000 people is $18. At this price, every
ticket is sold. A survey indicates that for every $2 increase per ticket, attendance will
drop by 500 people.
a) What is the maximum revenue?
b) What ticket price would result in the greatest revenue?
c) How many tickets must be sold to maximize the revenue?

Answer 1

Answer:

hello

Step-by-step explanation:

Revenue = number of tickets sold * cost of 1 ticket

When the price is $3, all 800 tickets are sold, bringing in a revenue of $2400.

Let x = number of $1 increases in the cost of a ticket

We are told that for every $1 increase in cost, there are 100 fewer attendees. So, if you make "x" increases of $1, the number of attendees will be

800 - 100x

Revenue when the cost of a ticket is $3 + x would be (800 - 100x)*(3 + x)

Let y = revenue.

y = (800 - 100x)(3 + x)

or,

y = 100(8 - x)(3 + x)

You've got an equation in the form

y = a(x - b)(x - c)

which is known as the "intercept form" for the equation of a parabola.

The x-intercept occurs

at x - b = 0, and x - c = 0....or, in your specific case, when 8 - x = 0 or when 3 + x = 0.

Ok....the vertex of the parabola (which is the maximum or minimum value of the function) occurs halfway between the x-intercepts.

I hope you can find the vertex, and thus the max or minimum value for the function.

make as brainllist

have a nice day

Answer 2

Answer:

Good evening

Revenue = number of tickets sold * cost of 1

ticket

When the price is $3, all 800 tickets are sold, bringing in a revenue of $2400.

Let x = number of $1 increases in the cost of a ticket

We are told that for every $1 increase in cost, there are 100 fewer attendees. So, if you make "x" increases of $1, the number of attendees will be

800 - 100x

Revenue when the cost of a ticket is $3 + x would be (800 - 100x)*(3 + x)

Let y = revenue.

y = (800 100x)(3 + x)

or,

y = 100(8 - x)(3 + x)

You've got an equation in the form

y = a(x - b)(x - C)

which is known as the "intercept form" for the equation of a parabola.

The x-intercept occurs

at x - b = 0, and x - c = 0...or, in your specific case, when 8 - x = 0 or when 3 + x = 0.

Ok.the vertex of the parabola (which is the maximum or minimum value of the function) occurs halfway between the x-intercepts.

I hope it's helpful for you