SOLUTION: A theater has 550 seats. The theater will sell tickets for all seats if the tickets cost $30 each. However, for each $4 increase in ticket price, 20 fewer tickets are sold. What t

Question 877332: A theater has 550 seats. The theater will sell tickets for all seats if the tickets cost $30 each. However, for each $4 increase in ticket price, 20 fewer tickets are sold. What ticket price will generate the most revenue and what is the maximum revenue?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A theater has 550 seats. The theater will sell tickets for all seats if the tickets cost $30 each. However, for each $4 increase in ticket price, 20 fewer tickets are sold. What ticket price will generate the most revenue and what is the maximum revenue?
***
let x=number of $4 increase in ticket prices
Revenue=price*number of tickets sold.
R=(30+4x)*(550-20x)
R=16500+1600x-80x^2
R=-80x^2+1600x+16500
complete the square:
R=-80(x^2-20x+100)+8000+16500
R=-80(x-10)+24500
x=10
number of $4 increase in ticket prices=10
maximum revenue will be generated when ticket price is increased by $40 to $70
maximum revenue =$24,500
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