Optimization Prob.:A 300-room hotel in Las Vegas is filled t

[stacytracey]

A 300-room hotel in Las Vegas is filled to capacity every night at $80 a room. For each $1 increase in rent, 3 fewer rooms are rented. If eash rented room costs $10 to service per day, how much should the management gross profit? What is the maximum gross profit?

I really dont understand how to setup this problem?
Please help!

 

[galactus]

Profit = Revenue - Cost.

\(\displaystyle R(x)=(80+x)(300-3x)\)

Differentiate, set to 0 and solve for x. Don't forget the cost of cleaning the rooms.

 

[stacytracey]

Thank for your help with this problem