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Quantitative Methods homework

Quantitative Methods homework

I need these questions answered completely. Tables are included. I need how you got the answer and an explanation included. Not just the answers. 

 

·         8-3 Durham Health Clinic is considering signing a contract to perform 50 pre-employment physicals per week for a specific corporation. In terms of staff time, a pre-employment physical requires 0.20 hours in Reception/Discharge, 0.45 hours in Nursing and Testing, and 0.20 hours in Medical Examination. By work-station, determine how many work hours per week will be needed to perform these physicals.

·         8-4 Currently the clinic does 250 visits per week, with 50% of all visits as return visits. Each employee (physician, nurse, and receptionist) is scheduled to work 35 hours per week.

    • a. How many employees by type does the clinic currently need?
    • b. How many employees by type will the clinic need if it signs the contract for pre-employment physicals?
    • c. If return visits shift to 10% of all regular visits, how many employees by type will the clinic need with and without the contract for pre-employment physicals?
    • d. How will the answers to “b” and “c” change if the number of physicals is modified to 35 pre-employment physicals per week?

Throughout these analyses, specify all assumptions, including assumptions concerning worker productivity.

  • 8-5 How would your answers change for problem 8-1 if nursing and testing time was increased to 0.50 hours for both first and repeat visits, and medical exam and treatment time was reduced to 0.30 hours for a first visit and 0.20 hours for a return visit?

 

 

                                          

  • 9-1 Alpha Walk-in Clinic operates as a single channel single server system. On Tuesdays, its average arrival rate (μ) per hour is 7.0. Analysis indicates that its service rate (λ) is 8.5 patients per hour. Using queuing theory, describe this service system. What is:
    • a. The probability that the clinic is idle—no patients waiting or being served?
    • b. The average number of patients in the system?
    • c. The average time (hours) a patient spends in the system (waiting + service time)?
    • d. The average number of patients in the queue waiting for service?
    • e. The average time (hours) a patient spends in the queue waiting?
    • f. The probability that the patient, upon arrival, must wait?
  • 9-2 The following data have been collected from a hospital pharmacy. This service system operates as a single server, single channel system.

 

7–3 pm

3–11 pm

11–7 am

Service rate per hour

200

100

50

Arrival rate per hour

 60

 50

40

  • The service rate can be increased or decreased in increments of 50 prescriptions per hour. The expense associated with each 50-prescription increment is $100. In other words, to be able to process 50 additional prescriptions will cost an additional $100 per hour. If the current rate of processing or service is lowered by 50 prescriptions per hour, the savings are $100 per hour. Using queuing theory, describe this service system. What is:
    • a. The probability that the clinic is idle—no patients waiting or being served?
    • b. The average number of patients in the system?
    • c. The average time (hours) a patient spends in the system (waiting + service time)?
    • d. The average number of patients in the queue waiting for service?
    • e. The average time (hours) a patient spends in the queue waiting?
    • f. The probability that a patient, upon arrival, must wait?

Given the associated costs, should the service rate be changed? What are the financial implications associated with your recommendations?

 

  • 10-2 In the clinic renovation example, what if management thinks that the likelihood of current demand remaining is 30%, the likelihood of a moderate increase is 25%, and the likelihood of a large increase is 45%? What should they do, according to the expected total payoff?

·         An ambulatory care clinic administrator is trying to decide whether to renovate to accommodate possible increased demand. The manager could plan a major renovation costing $700,000 that would allow 50 patients per day to be served, or a minor renovation costing $225,000 that would allow 35 patients a day to be served. The final alternative is to do nothing, thus keeping the status quo by not renovating. This continues the existing capacity of accommodating the current 20 patients per day, but no more. Presently the clinic earns $75 per patient served. Assume that the clinic is open 300 days per year and that management wants to cover the costs of the renovation from first-year earnings.

·         To begin quantitatively analyzing our decision options, we first go back to the three decision steps listed previously. The first step is to state the alternatives. These are to do nothing, undergo a minor renovation, or undergo a major renovation. The second step is to determine the future states of the world. These are the unknowns in our decision. Here they are the estimates of future demand. Because our decisions limit future capacity, we will use these limits as estimates of future demand. Thus, let us describe the potential for 20 patients per day, 35 patients per day, or 50 patients per day to be served, defined by current capacity, capacity given a minor renovation, and capacity given a major renovation.

·         There are three alternatives and three possible states of the world. This means that there are nine possible outcomes. These are listed in Table 10-3. The third step is to determine the payoffs for each of the potential outcomes.

·         Earnings are based upon patients served; therefore, part of the payoff involves earnings. For each state of the world of future demand, there are different potential maximum patients who can be seen. Each of these brings in revenue of $75. This amount is then multiplied by the 300 days the clinic is open yearly to calculate the total revenue per year. The maximum revenue generated in each state of the world can be seen in Table 10-4.

·         Table 10-3 Expected Outcomes for Clinic Renovation

Alternative

State of the world (future demand forecasts)

Outcome

No renovation/do nothing

Demand remains at 20 patients per day

Demand is met

No renovation/do nothing

Demand increases to 35 patients per day

Demand is not met

No renovation/do nothing

Demand increases to 50 patients per day

Demand is not met

Minor renovation

Demand remains at 20 patients per day

Demand is met

Minor renovation

Demand increases to 35 patients per day

Demand is met

Minor renovation

Demand increases to 50 patients per day

Demand is not met

Major renovation

Demand remains at 20 patients per day

Demand is met

Major renovation

Demand increases to 35 patients per day

Demand is met

Major renovation

Demand increases to 50 patients per day

Demand is met

 

 

  • 12-1 Using the information in Table 12-7, construct a PERT network and answer each of the following questions:
    • a. What is the expected project completion data?
    • b. What is the scheduled start and completion date for each activity?
    • c. Which activities are on the critical path?
    • d. How long can noncritical path activities be delayed without jeopardizing the overall completion date for this project?
  • 12-2 Assess the impact of the following changes to the time estimates provided in question 12-1. Individually, what is the impact if:

Activity

Predecessor

New Time Estimate

O. Advertise for new staff

N

4

P. Interview for new staff

O

6

Q. Select new staff

P

1

Collectively, what is the impact of these changes?

  • 12-3 As project manager for the example included in question 12-1, what would you recommend to preserve the original project completion date if activity A was reestimated to take 8 weeks, not the original 4 weeks? Provide details.

Table 12-7 Project to Convert a 20-Bed Unit in a Nursing Home to Accommodate Patients with Dementia

Activity

 

Predecessor

Time estimate (weeks)

A

Secure state approval

4

B

Identify 20-bed unit to be used

A

1

C

Move existing residents

B

1

D

Clean space

C

2

E

Develop architectural plans

A

9

F

Install new heating and ventilation systems

E

4

G

Install security systems

E

2

H

Move walls; renovate

F

4

I

Identify new equipment

A

1

J

Order new equipment

I

1

K

Unpack and inspect new equipment

J

1

L

Install new equipment

D, K, H

3

M

Reassign staff

A

1

N

Identify new staffing needs

M

1

O

Advertise for new staff

N

3

P

Interview for new staff

O

2

Q

Select new hires

P

3

R

Develop care plan protocols

M

1

S

Train staff

R, Q, M, L

1

T

Modify quality assurance plans

S

2

U

Coordinate with hospital discharge planners

T

4

V

Complete internal audit

U, G

1

 

 

  • 13-1 A representative of a reputable financial services company has approached you as manager of a four-person group of anesthesiologists with an opportunity to purchase a 10-year annuity due for each member of the group. The annuity due would pay $40,000 each year beginning 5 years from now (i.e., at time = 5). What is the most you would be willing to pay now, per each physician, for this investment? Assume an appropriate discount rate of 7%.
  • 13-2 The hospital’s marketing and finance departments have just provided you, as chief financial officer, with pro forma income statements for your proposed sonogram center. These statements appear in the following. Pro forma Income Statement (000)

Time

t + 1

t + 2

t + 3

t + 4

Service Revenues (net)

$425

$500

$580

$700

Expenses

$400

$450

$525

$600

Depreciation Expense

$ 35

$ 35

$ 35

$ 35

Net Income

($ 10)

$ 15

$ 20

$ 65

  • What is the project’s IRR? Assume an initial investment of $175,000 and an appropriate discount rate of 6%. The hospital is operated as a not-for-profit facility.
  • 13-3 The chief operating officer (COO) of a small, not-for-profit community hospital has to make a recommendation to the board of trustees on choosing among three project options for an unrestricted gift of $250,000 that has just been received. The board has established a time horizon of 5 years on this project. The options are described in the following.
    • a. Purchase a 5-year treasury note at an interest rate (annual) of 7%.
    • b. Purchase the practice of a young physician (the hospital’s third highest admitter). Estimates of projected cash flows for the practice (post-purchase), are: Probability of Cash Flow

Time

60%

20%

20%

t + 1

$ 40,000

$20,000

$ 60,000

t + 2

$ 60,000

$30,000

$ 80,000

t + 3

$  75,000

$40,000

$100,000

t + 4

$100,000

$50,000

$125,000

t + 5

$100,000

$50,000

$125,000

    • c. Purchase an upgraded analyzer for the laboratory. Based on forecasts of laboratory utilization, the net cash flows for this project are:

Time

Net Cash Flow

t + 1

$75,000

t + 2

$75,000

t + 3

$50,000

t + 4

$50,000

t + 5

$50,000

    • Which investment should the COO recommend and why?

 

 

 

 


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