/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} 12OQ L. Winston Martin (an allergist)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: 12OQ (page 254)

L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two nurses. The special injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day, patient load drops, and only one nurse is needed to administer the injections. Let鈥檚 focus on the simpler case of the two鈥攏amely when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an inter-arrival time of approximately three minutes. It takes the nurse an average of two minutes to prepare the patients鈥 serum and administer the injection.

a.What is the average number you would expect to see in Dr. Martin鈥檚 facilities?

b.How long would it take for a patient to arrive, get an injection, and leave?

c.What is the probability that there will be three or more patients on the premises?

d.What is the utilization of the nurse?

e.Assume three nurses are available. Each takes an average of two minutes to prepare the patients鈥 serum and administer the injection. What is the average total time of a patient in the system?

Short Answer

Expert verified

Expect customer arrival to be Poisson conveyed and benefit from being exponentially distributed.

Arrival鈥rate鈥鈥位=1鈥per鈥鈥3min鈥=鈥20鈥per鈥hour.Service鈥鈥rate鈥鈥渭鈥=鈥1鈥in鈥2min鈥=鈥30鈥per鈥hour.

Step by step solution

01

(a) Calculate the Average number of patients waiting in the system as follows: Average number of patients waiting in the

Ls鈥=鈥位渭-位Ls鈥=鈥2030-20Ls鈥=鈥2

The average numberof patients expected is 2

02

(b) Calculate the average total time in the system as follows The average total time in the system

Ws=鈥Ls位鈥鈥鈥鈥鈥鈥鈥=220鈥鈥鈥鈥鈥鈥鈥=鈥6鈥minutes

Hence, the average total time for a patient 6 is minutes.

03

(c) The probability that 3 or more patients are present with the help of the given formula is as follows:

The probability that 3 or more patients are in the hospital is

P=1-probability鈥that鈥less鈥3鈥patients鈥are鈥in鈥the鈥hospitalP=1-probability鈥that鈥less鈥3鈥patients鈥are鈥in鈥the鈥cafeteriaP=1-P0鈥+P1+P2

Pn鈥=鈥1-位渭位渭n

渭=Rate鈥of鈥service鈥delivery位鈥=鈥Rate鈥of鈥customer'鈥arrival

n=0,P0鈥=鈥0.3333n=1,P1鈥=鈥0.2222n=2,P2鈥=鈥0.1481

Substitute the above values in the following results. The probability that 3 or more people are in the cafeteria

P=1-0.3333+0.2222+0.1481鈥鈥鈥鈥鈥鈥鈥鈥=鈥鈥0.2963

Hence, the probabilitythat 3 or more people are in the cafeteria is 0.2963

04

(d) Calculate the percentage of time utilization with the help of the given formula

Percentage of time utilization

蚁=位渭

p = Percentage of time utilization

渭 = Rate of service delivery

位 = Rate of customers' arrival

role="math" localid="1650530359967" 位=20鈥per鈥minutes渭鈥=鈥30鈥per鈥minutes

Substitute the above values in the following results:

蚁鈥=鈥2030鈥鈥鈥鈥鈥鈥鈥鈥=0.66鈥or鈥66.7鈥%鈥鈥of鈥the鈥time

Hence, the percentage of time utilization is

0.66 Or 66.67% of the time

05

(e) Calculate the average total time of patients in the system as follows

Assume there are 3 servers, that is,s鈥=鈥3鈥and鈥蚁鈥=鈥0.667

Refer to the table "Expected number of customers waiting in line for various values of s" given in the chapter.

Thus, the expected number of customers waiting in line Lqs=3and蚁=0.667will be between 0.0084 and 0.0112.

Take the average of two values (0.0084 and 0.0112) which will be 0.0093

Calculate the average total number of patients in the system Ls as follows:

Ls鈥=鈥Lq+位渭鈥鈥鈥鈥鈥=鈥0.0093+0.667鈥鈥鈥鈥鈥=鈥0.6763

Therefore, the average total time spent in the system Wswill be

Ws=Ls位鈥鈥鈥鈥鈥鈥=鈥0.676320鈥鈥鈥鈥鈥=鈥0.0338鈥hours

Hence, the average total time of patient spent in the system is 0.338 hours or 2.028 min.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A book publisher has fixed costs of \(300,000 and variable costs per book of \)8.00. The book sells for $23.00 per copy.

a. How many books must be sold to break even?

b. If the fixed cost increased, would the new break-even point be higher or lower?

c. If the variable cost per unit decreased, would the new break-even point be higher or lower?

You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows for the three different classes of service. Each class of service would be separate with its cashiers and customers. Oddly enough, each class of service, while different, has the same demand and service times. People for one class of service arrive every four minutes, and arrival times are exponentially distributed (The standard deviation is equal to the mean). It takes seven minutes to service each customer, and the standard deviation of the service times is three minutes. You assign two cashiers to each type of service.

  1. On average, how long will each line be at each of the cashier windows?
  2. On average, how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is complete)? You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times.
  3. What will happen to the amount of time each cashier spends idle? (Increase, decrease, stay the same, depend on ________)
  4. What will happen to the average amount of time a customer spends in the bank? (Increase, decrease, stay the same, depend on ________)

Question:The following table lists all costs of quality incurred by Sam鈥檚 Surf Shop last year. What was Sam鈥檚 appraisal cost for quality last year?

Annual inspection cost

\(155,000

The annual cost of scarp materials

\)286,000

Annual rework cost

\(34,679

The annual cost of quality training

\)456,000

Annual warranty cost

\(1,546,000

Annual testing cost

\)543,000

An assembly line is to operate eight hours per day with the desired output of 240 units per day. The following table contains information on this product鈥檚 task times and precedence relationships:

Task

Task Time (seconds)

Immediate predecessor

A

60

-

B

80

A

C

20

A

D

50

A

E

90

B,C

F

30

C,D

G

30

E,F

H

60

G


  1. Draw the precedence diagram.
  2. b.What is the workstation cycle time required to produce 240 units per day?
  3. Balance this line using the longest task time.
  4. What is the efficiency of your line balance, assuming it is running at the cycle time from part (b)?

Question: The following represents a process used to assemble a chair with an upholstered seat. Stations A, B, and C make the seat; stations J, K, and L assemble the chair frame; station X is where the two subassemblies are brought together; and some final tasks are completed in stations Y and Z. One worker is assigned to each of the stations. The line is paced using a countdown clock to synchronize production at each station.

Generally there is no inventory kept anywhere in the system, although there is

room for one unit between each of the stations that might be used for a brief amount of time.

Given the following amount of work in seconds required at each station:

a

38

j

32

x

22

b

34

k

30

y

18

c

35

l

34

z

20

a. What is the possible daily output of this 鈥減rocess鈥 if 8 hours of processing time is available each day?

b. Given your output rate in part (a), what is the efficiency of the process?

c. What is the flow time of the process?
See all solutions

Recommended explanations on Business Studies Textbooks

Business Case Studies

Read Explanation

Change Management

Read Explanation

Business Development

Read Explanation

Managerial Economics

Read Explanation

Startups

Read Explanation

Sales in Business

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.