Maximum and minimum quadratics

[AO2005]

I am not quite sure where to start with this problem.

A large hotel has 250 rooms. mangementt has determined that if they charge $150 per room on Saturday night, they will book 210 rooms. For every $15 increase in the room price, 10 less rooms will be booked. What price should the hotel charge to maximize their revenue?

 

[lev888]

I am not quite sure where to start with this problem.

A large hotel has 250 rooms. mangementt has determined that if they charge $150 per room on Saturday night, they will book 210 rooms. For every $15 increase in the room price, 10 less rooms will be booked. What price should the hotel charge to maximize their revenue?

Start with the expression for the total revenue as a function of the room price. The use methods you've been taught to find its maximum.

 

[Steven G]

$150 --------------210 rooms
$150 +$15*1------210 - 10*1
$150 +$15*2------210 - 10*2
$150 +$15*3------210 - 10*3
....
$150 +$15*x------210 - 10*x