Consider an orthopedist's office in Chapel Hill. All arriving patients first check in at a reception area where they fill out the necessary paperwork. On average, it takes 10 minutes to complete check-in and there are four receptionists working at the office. Then the patients are seen by a doctor. An average exam takes 30 minutes to complete there are ten doctors working at the office. 40% of the patients do not need further evaluation after the exam and proceed to the reception area for check out. The remaining 60% require X-rays. X-rays are taken by the X-ray technician. It takes on average 20 minutes to process a patient at the X-ray machine and there are three X-ray technicians and three X-ray machines.Once the X-rays are complete, the patient is seen by a doctor again who finalizes the diagnosis by looking at the X-ray. It takes on average 22 minutes for the doctor to evaluate the X-ray and finalize the diagnosis after which the patient goes to the reception area for check out. It takes 5 minutes for a receptionist to check a patient out.

a. What is the capacity of the orthopedist's office in patients/hour? Which resource is the bottleneck?

b.Now assume that after evaluating the X-rays, the orthopedist rejects some of them because their contrast index is outside the specified tolerance limits where the lower and upper tolerance limits are set at 1.45 and 1.60 respectively. The average contrast index for X-ray machines at the office is 1.50 and the standard deviation is 0.05. Compute the percentage of X-rays that will be rejected by the doctors.

c.If a patient's X-ray is rejected (at the end of the 22-minute evaluation by the doctor), she has a second X-ray taken (assume that the second X-ray will always be accepted) and this new X-ray must be evaluated by the doctor before the patient receives a diagnosis and proceeds to check-out. It takes the doctor 22 minutes to evaluate the new X-ray and provide a final diagnosis. Assuming 25% of X-rays are rejected, what is the capacity of the orthopedist's office in patients/hour? You should ignore your calculation from part (b) to answer this question.

d. Assume that the net profit the doctor's office makes on a patient is $50. Recalibrating the three X-ray machines at a cost of $25,000 will ensure that the contrast index of all X-rays will fall within the tolerance limits. How long will the payback period be for this investment? Assume that the orthopedist's office is open eight hours a day, five days a week, and 50 weeks a year.