The Restwell Motel in Orlando, Florida, is preparing an aggregate plan for the upcoming $12$ days. The motel has a maximum of $200$ rooms, but demand varies during the week. Demand is listed in terms of rooms rented each day. The motel requires one employee, paid $$105$ per day for each $12$ rooms rented. It can utilize up to $20$ percent overtime at $150$ percent pay and also can hire part$-$time workers at $$120$ per day. Each part$-$time worker can also clean $12$ rooms per day. There is no hiring and layoff cost for the part$-$time workers. A fractional number of part$-$time workers $($e$.$g$.,3\mathrm{.}4$ workers$)$ can be employed since less than a full day of employment is possible for each worker.