Part a$)$ How would you modify the model to imply that, during the rescheduling time horizon, at most a total of $20$ part$-$time nurses could be hired for all units? $(3$ points$)$

Part b$)$ The hospital has some financial problems, and therefore the management of the hospital has decided to limit the extra payments to on$-$call nurses. More specifically, each unit of the hospital is not supposed to pay more than $$2000$ to on call nurses, during a rescheduling time horizon. Supposing that the duration of each time slot in the given model is $2$ hour and on$-$call nurses are paid $100$$$/$hour$,$ write a constraint to formulate the requirement on limiting the budget for on$-$call nurses. $(3$ points$)$

Part c$)$ During the rescheduling time horizon, each nurse is allowed to work in only one of the units. How would you modify the model to imply this constraint? $(4$ points$)$

Part d$)$ For each unit, the number of on$-$call nurses that start to work during the rescheduling time horizon cannot be $10$ units more than the average number of on$-$call nurses in all units during the rescheduling time horizon. How would you modify the model to imply this constraint? $(3$ points$)$

Part e$)$ The total number of part$-$time nurses working in time slot $8$ in any unit must be at most $10$ persons. How would you modify the model to imply this constraint? $(3$ points$)$