SOLUTION: hey hi, A theatre seats 2000 people and charges $10 for a ticket. At this price, all the tickets can be sold. A survey indicates that if the ticket price is increased, the numbe

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: hey hi, A theatre seats 2000 people and charges $10 for a ticket. At this price, all the tickets can be sold. A survey indicates that if the ticket price is increased, the numbe      Log On


   

Question 112292: hey hi,
A theatre seats 2000 people and charges $10 for a ticket. At this price, all the tickets can be sold. A survey indicates that if the ticket price is increased, the number sold will decrease by 100 for every dollar of increase. what ticket price would result in the greatest revenue?
And thank you.
i will be waiting!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
revenue=(tickets)*(price) ___ let x="price increase"

r=(2000-100x)(10+x) ___ r=20000+1000x-100x^2

the graph of this is a downward opening parabola ___ the maximum is on the axis of symmetry

x=-b/2a ___ x=-1000/((2)(-100))


if you want, you can find the revenue by substituting the x value into the r equation