Part $1$:

You are asked to perform capacity analysis for a local clinic. The current resources of the clinic are as follows:$$Resource

Number of service providers available$$Reception $4$ Primary care provider $8$ Nurse $8$ Dermatology $2$ Diabetes care $2$ Nutrition care $1$

You are also given the following information:

$$ All patients need to register with the receptionist before they can see a nurse or a doctor. The average time at the reception desk is $3$ minutes.

$$ On average

o $20\%$oftheincomingpatientsareconsideredtohaveonlyminorproblemsthatcan

be handled by nurses.

o $50\%$ofpatientsseeaprimarycareprovider

o $10\%$ofpatientsseeadermatologist

o $15\%$ofpatientsseeadiabetescarespecialist o $5\%$ofpatientsseeanutritionist.

$15\%$ of all patients need to see the receptionist to schedule their next appointment after seeing their nurse or doctor. The average time to do so is $5$ minutes.

$$ The average appointment time with each provider is: o Nurse:$15$minutes

o PrimaryCare:$30$minutes o Dermatology:$45$minutes o DiabetesCare:$40$minutes o Nutritioncare:$30$minutes

$$ Assume that a typical workday is $10$ hours. Reception workers spend half of their time checking$-$in patients and scheduling new appointments, nurses spend $25\%$ of their time seeing patients, and primary care and specialty clinics spend all their time seeing patients. For reception and nurses, their remaining time is spent on other tasks.

$$ Assume $175$ patients arrive per day.

Based on the above information, answer the following questions:

$1)$ What is the capacity of each resource in terms of number of patient arrivals$/$day$?(18$ points$)$

$2)$ Which resource is the bottleneck? $(3$ points$)$

$3)$ What is the total system capacity in terms of number of patient arrivals$/$day$?(3$ points$)$

$4)$ What is the utilization of each resource? $(6$ points$)$