Part $2$ Vaccine $(3*0\mathrm{.}5=1\mathrm{.}5$ points$)$ In an unexpected turn of events, you are now part of an undergraduate student team responsible for designing the Covid$-19$ vaccination process at Georgia Tech. After some discussion, your team designs a process for each vaccination site that consists of four stages: $$ Stage $1($Check$-$in$)$ Employees and students $($the patients$)$ arrive at the vaccination site, present their IDs, are verified for eligibility, and registered into a database. Based on data from other vaccination sites, you estimate that $15\%$ of people who arrive will be turned away after the eligibility check and do not proceed to Stage $2.$ Stage $2($Health Questionnaire$)$ After check$-$in$,$ eligible patients a few basic health$-$related questions $($if they had Covid$-19$ recently, if they have allergies, etc$)$ and have their temperature measured. Depending on the outcome of the questionnaire, the patient might receive a recommendation to consult with their physician before taking the vaccine and leave the vaccination process. You estimate that $5\%$ of patients who enter Stage $2$ are recommended to consult with a physician before taking the vaccine and do not proceed to Stage $3($they leave the vaccination process$).$ Stage $3($Vaccination$)$ After responding to the health questionnaire in Stage $2$ and being cleared for the vaccination, the patient proceeds to the vaccination area where the vaccine is applied. $$ Stage $4($Recovery and Observation$)$ Vaccinated patients are then taken to a rest area where they are observed for some time to make sure no allergic reaction occurs, answer some follow$-$up questions, and schedule their second vaccine appointment if needed. Each vaccination site will be managed and run by a team of $6$ employees with basic healthcare training. These employees are completely cross$-$trained and can work at any stage. Due to social distancing guidelines, each stage occurs in a separate room and there is no "inventory" of people between stages $($the vaccination process is a continuous flow process like the questions in Assignment $3).$ Furthermore, if an employee is allocated to a stage at the beginning of the day, they cannot switch stages on the same day. For example, an employee allocated to Stage $2$ at the start of the day cannot switch to Stage $4$ until the next day. Furthermore, each employee will work in only one stage per day. You estimate that: a single employee can $$ Check$-$in $40$ people per hour if they work in Stage $1($thus$,$ x employees can check$-$in x$*40$ people per hour$),$ Conduct $18$ health questionnaires per hour if they work in Stage $2,$ Vaccinate $10$ patients per hour if they work in Stage $3,$ or $$ Observe $15$ patients per hour if they work in Stage $4.$ Assume that each stage must have at least one employee. Given this setup, please answer the following questions. Question $5$ How many of the $6$ employees would you allocate to each of the four stages to maximize the output capacity of this process? What is the vaccine process capacity $($in patients per hour$)$ for this allocation? Recall that each stage must have at least one employee. Note: An example of an employee allocation would be two employees in Stage $1,$ one employee in Stage $2,$ one employee in Stage $3,$ and two employees in Stage $4.$ Another example is one employee in Stage $1,$ one employee in Stage $2,$ one employee in Stage $3,$ and three employees in Stage $4.$ Your goal is to propose an allocation that maximizes system capacity. a$.1$ employee, $2$ employees, $1$ employee, $2$ employees b$.1$ employee, $1$ employee, $2$ employees, $2$ employees c$.2$ employees, $1$ employee, $2$ employees, $1$ employee d$.2$ employees, $2$ employees, $1$ employee, $1$ employee Question $6$ For your employee allocation in Question $5,$ what is the utilization of the vaccination process $($stage $3)$ when the process is running at maximum capacity? Question $7$ One of your teammates proposes to create a pre$-$screening health questionnaire with a few questions. You estimate that the pre$-$screening questionnaire would reduce the fraction of patients that leave at Stage $2($i$.$e$.$ they enter Stage $2$ but do not continue to Stage $3)$ from $5\%$ to $0\%.$ What is the vaccine process capacity $($units in patients$/$hr$)?$