Double Tree Hilton is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:

Rental Class

Super Saver

Deluxe

Business

Room

Type I

$$30$

$$35$

$$50$

Type II

$$20$

$$30$

$$45$

Double Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class.

The demand forecast for a particular night is $120$ rentals in the Super Saver class, $60$ in the Deluxe class, and $30$ in the Business class. $($These demands are the maximum numbers to accept for each rental class. The actual reservation may be less.$)$ Double Tree has $100$ Type I rooms and $130$ Type II rooms. What is the maximum profits$($$$)?$ What is the number of reservations accepted in super saver for Type II rooms?