Posted by **Ak** on Tuesday, November 3, 2009 at 12:43am.

The Green Mountain Inn can rent all its 210 rooms when it charges $45 per night for a room, but the manager wants to increase profits. He finds, however, that for each $2 increase in the room rate, 3 fewer rooms are rented. If the cost of cleaning an occupied room is $5 per night, what should the manager charge per night for a room to maximize profits?

- Math, not "12" -
**Writeacher**, Tuesday, November 3, 2009 at 4:46am
Assistance needed.

Please type your __subject__ in the **School Subject** box. Any other words are likely to delay responses from a teacher who knows that subject well.

- 12 -
**Reiny**, Tuesday, November 3, 2009 at 7:50am
Let the number of $2 increases be n

Now:

number of rooms = 210

cost per room = 45

cost of cleaning= 210(5)

After increase:

number of rooms = 210 - 3n

cost per room = 45 + 2n

cost of cleaning = 5(210-3n)

profits = (210-3n)(45+2n) - 5(210-3n)

= ...

expand the above, then express as a simplified quadratic.

If you know Calculus, differentiate and set equal to zero to solve for n

If you are doing these by completing the square, do so.

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