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?
Answers
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:
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