For example, the first row of the table shows that $34$ people checked in on Monday and were in the hospital for Monday, Tuesday, and Wednesday. By summing the column of the table for Wednesday, we see that there are $102$ patients staying in the hospital that day.

The medical facilities at Shouldice consist of four operating rooms, a patient recovery room, a laboratory, and six examination rooms.

Now look at the effect of increasing the number of beds by $50$ percent.

a$.$ How many operations could the hospital perform per day before running out of bed capacity? $($Assume operations are performed five days per week, with the same number performed on each day.$)$

Note: Round your answer to the nearest whole number.

Number of operations per day

c$-1.$ In order to fill the beds as calculated in part a$,$ how many hernia repair operations would need to be performed in each operating room each day? $($Since it makes no sense to perform just a part of an operation, round your answer up to the next whole number if necessary.$)$

Operations per operating room per day

$c-3.$ To fill the beds as calculated in part a$,$ how many hernia repair operations would each surgeon need to perform each day? $($Since it makes no sense for a surgeon to perform just a part of an operation, round your answer up to the next whole number if necessary.$)$

Operations per surgeon per day

c$-5.$ Based on the current scheduling practices with the $50\%$ addition to bed capacity, what is the maximum number of hernia repair operations that the hospital could perform each week without exceeding its capacity limits$?($Hint$.$ Consider the capacities of the beds, operating rooms and surgeons.$)$

Maximum number of operations p$$r weekShouldice Hospital in Canada is widely known for one thing$-$hernia repair! In fact, that is the only operation it performs, and it performs a great many of them. Over the past two decades this small $102-$bed hospital has averaged $7,960$ operations annually. Last year, it had a record year and performed nearly $8,460$ operations.

A hernia repair operation at Shouldice Hospital is performed by one of the $12$ full$-$time surgeons assisted by one of seven part$-$time assistant surgeons. The first operations begin at $7$:$30$ AM each day, Monday through Friday. Surgeons generally take about one hour to prepare for and perform each hernia operation, and they operate on an average of at most four patients per day. This four patient per day limit on the average number of operations performed per surgeon has been found to be the best operating level for the hospital as it takes into account the time the surgeons need for patient exams and consultations, updating medical charts, writing reports, traveling to professional conferences, vacations, and other times when they are performing other duties or are not available to perform surgeries. A given surgeon may perform more than four surgeries on a given day, but the average cannot exceed four without having adverse effects on overall hospital operations. The surgeons' day ends at $4$ p$.$m$.$ Although hernia repair operations are performed only five days a week, the remainder of the hospital is in operation continuously to attend to recovering patients.

The table below is a room$-$occupancy table for the existing system. Each row in the table follows the patients who checked in on a given day. The columns indicate the number of patients in the hospital on a given day.

$\backslash$table$[[,$BEDS REQUIRED$],[$CHECK$-$IN DAY,MONDAY,TUESDAY,WEDNESDAY,THURSDAY,FRIDAY,SATURDAY,SUNDAY$],[$Monday$,34,34,34,,,,],[$Tuesday$,,34,34,34,,,],[$Wednesday$,,,34,34,34,34,],[$Thursday$,,,,34,34,34,],[$Friday$,,,,,,,],[$Saturday$,,,,,,,34],[$Sunday$,34,34,,,,34,34],[$Total$,68,102,102,102,68,34,],[,,,,,,,],[,,,,,,,]]$

For example, the first row of the table shows that $34$ people checked in on Monday and were in the hospital for Monday, Tuesday, and Wednesday. By summing the column of the table for Wednesday, we see that there are $102$ patients staying in the hospital that day.