Question

Help please >.<
The Hotel Lakewell has 450 rooms. Currently the hotel is filled . The daily rental is $ 750 per room.
For every $ 4 increase in rent the demand for rooms decreases by 7 rooms.
Let x = the number of $ 4 increases that can be made.
- What should x be so as to maximize the revenue of the hotel ?
- What is the rent per room when the revenue is maximized? $
- What is the maximum revenue? $

Answer 1

number of rooms rented = 450 - 7x
price per room = 750 + 4x

revenue = (450-7x)(750+4x)
expand, then either find the vertex of the resultiong quadratic function, or
differentiate, set equal to zero, and solve for x

Answer 2

revenue is demand*price
r(x) = (450-7x)(750+4x)
Hmmm. I get max revenue when x = -61.
Sure those figures are right?
Sure my function looks good?