Sam is the group sales manager at the $400-$room full$-$service Hilton Hotel. Tyla is the front of$$ce manager. Together with James, the GM$,$ they make the revenue management decisions for their property. For the Friday night that is just one week away, they have $180$ unsold rooms remaining. Sam would like to accept an available group contract for the entire $180$ rooms. $$We$$ll sell out,$$ he proclaims, $$and have a great RevPAR.$$ Tyla would like to reduce the room rates to $$159\mathrm{.}00$ per night; which is a $$20\mathrm{.}00$ reduction from the hotel$$s normal rate of $$179\mathrm{.}00$