Identify the problem, objective, constraints and decision variables in the following case, as well as writing the constraints and objectives in terms of decision variables.

A large hotel chain aims to optimize its pricing and room allocation strategy to maximize revenue. The hotel has a limited number of rooms of various types $($standard$,$ deluxe, and suite$)$ and faces varying demand throughout the year.

For the upcoming year, the availability of different room types is as follows:

$-$ Number of standard rooms: $100$

$-$ Number of deluxe rooms: $50$

$-$ Number of suites: $20$

The total number of available rooms is $170.$ The allocation for each room type must not exceed these availabilities.

The manager has reviewed past data and experiences to set the price range for each type of room:

$-$ Standard room: $$100-$ $$200$

$-$ Deluxe room: $$150-$ $$300$

$-$ Suite: $$250-$ $$500$

To cover operational costs, the manager requires a minimum occupancy rate of $70\%.$

The manager now seeks to determine how to dynamically adjust room prices and allocate rooms efficiently to maximize profit.