$2.$ For these next questions, assume the following: $-$ Every patient spends $4$ days in the hospital. So$,$ for instance, a patient that is admitted on Sunday morning will leave Thursday morning. $-$ Patients are only admitted Sunday through Thursday $($disregard any other dates mentioned$)-$ Hernia operations are only performed Monday through Friday. $-$ The $14$ additional hostel rooms can hold only one patient each. $-$ A patient may stay in a hostel room only on his first night, i$.$e$.$ before the operation. $-$ There are only $89$ regular hospital beds. $-$ The surgery teams can collectively perform no more than $37$ operations in a single day, assuming operating rooms are available. $-137$ patients are operated on per week. $($We calculate $137$ patients$/$week from $6850$ patients$/$year in $1982$ with $50$ operating weeks$/$year$.)-\backslash (20\backslash \%\backslash )$ of patients require a general anesthetic. $($a$)$ Compute the annual net profit of clinic and hospital operations $($separately$).$ The clinic performs operations, and the hospital maintains the beds. Which more profitable? $($b$)$ Use Little's Law to compute the average number of beds occupied. $($c$)$ Develop a weekly schedule of admittances and discharges that achieves a weekly throughput $>=137$ patients without violating any major resource constraints. Develop your weekly schedule using a table something like the following: Note that you should assume that each week follows the same schedule of admittances, departures, etc. Confirm that the average number of beds occupied overnight equals the average you computed in $(2$b$).$