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 $12,280$ operations annually. Last year, it had a record year and performed nearly $12,780$ 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 pertorm 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.CHECK$-$IN DAYTHURSDAY FRIDAY SATURDAY SUNDAY$10234$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 seven 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 dayb. What would the utilization of the bed capacity become if the new beds were added and the hospital were to perform the number of operations calculated in part a$?$Note: Round your answers to $1$ decimal place.How well would the new resources be utilized relative to the current operation?With the increase in beds and operations, the bed utilization $\_$ current hospital operations.relative to thec$-1.$ 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.$)$Joeratons per operating room per dayc$-2.$ Based on the current scheduling practices, does the hospital have enough operating room capacity for the number of operations required to fill the available beds as calculated in part a$?($Assume that the time to clean and set up an operating room between operations is insignificant compared to the time required for an operation.$)$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.$)$c$-4.$ Based on the current scheduling practices, does the hospital have enough full$-$time surgeons to perform the operations required to fill the available beds as Calculated in part a