operation research question paper madras university

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Madras University Question Papers: PDF Download Links

Updated On: March 01, 2024 01:44 pm IST

Madras University Question Papers: Key Highlights

• Madras University Question Papers: UG and PG Sample Papers (Links …

Madras University Question Papers: Steps to Download

Madras university question papers: university subject code (pdf links available), madras university question papers: advantages.

Madras University Question Papers: Students preparing for semesters at  Madras University  find the previous year's question papers as a useful resource. Crafted to align with the syllabus, these papers provide insights into examination patterns and focus areas. Accessible in PDF format via the university's official website, they offer invaluable preparation material for students.

Established in 1857, the University of Madras is a renowned institution fostering academic excellence. The University provides over 230 programs, including UG, PG, PG Diploma, Diploma, and Certificate courses across 87 academic departments grouped under 18 schools. These programs span Sciences, Social Sciences, Humanities, Management, and Medicine. The university has 121 affiliated colleges and 53 research institutions. Admission to University of Madras courses is either based on merit or through entrance exams. Additionally, the university offers distance education programs in Arts and Science through its dedicated centre.

This article serves as a valuable repository for Madras University question papers, including those for postgraduate, undergraduate courses, and distance courses. Students preparing for semester examinations can easily find and download these resources from the provided links.   Also Read:

Madras University question papers are tailored to specific courses, eliminating the need for students to sift through irrelevant material. Here are key highlights about Madras University question papers:

Madras University Question Papers: UG and PG Sample Papers (Links Available)

In the sections below, candidates will find links to Madras University question papers for UG, PG, and Distance education courses for the University of Madras exams. Explore these sections to access previous year's papers, facilitating your preparation for Madras University exams.

Madras University Question Papers: UG Course Wise Download

Candidates looking for Madras University question papers for undergraduate courses can find the links to the courses in the table below. It should be noted that candidates need to enter the respective course code to access the official pdf of the question paper:

Madras University Question Papers: PG Course/Masters Course Wise Download

Candidates looking for Madras University question papers for postgraduate/master courses can find the links to the courses in the table below. It should be noted that candidates need to enter the respective course code to access the official PDF of the question paper.

Madras University Question Papers: Distance Education Course Wise Download

The University of Madras established the Institute of Distance Education (IDE) in 1981 to support learners in reaching their educational, career, and personal objectives. With over 25 years of experience, IDE now offers 16 undergraduate courses, 22 postgraduate courses under the CBCS Pattern, 19 diploma courses, and 16 certificate courses.

To access Madras University's previous year question papers, students can follow these six step-by-step instructions provided below:

• Step 1: Navigate to the official website of Madras University.
• Step 2: Click on the "Examinations" tab.
• Step 3: Select "Previous Question Papers" from the dropdown menu.
• Step 4: On the new page, enter the subject code and click on the search button.
• Step 5: A list of Madras University previous question papers, categorized by subject, will appear.
• Step 6: Download the question papers PDF corresponding to the desired course or subject.

The University of Madras has issued distinct subject codes for various streams, and students can locate the subject-wise codes within their respective streams. The subject code PDF files for Madras University are available for download on the university's official website, or candidates can simply access the direct link below:

Steps to Download the Subject Code PDF files from the Official Website

For candidates trying to access the Subject code PDF file from the official website can follow the steps listed below:                     

• Step 1: Visit the official website of the University of Madras.
• Step 2: Select the 'Examination' section on the Madras University homepage.
• Step 3: From the examinations drop-down menu, choose the third option, 'CBCS UG Subject Code.'
• Step 4: On the CBCS UG Subject Code page, students can access PDF files containing subjects and subject codes for Bachelor's programs.
• Step 5: Click on the respective programs in Science, Arts, and Commerce under the CBCS pattern.
• Step 6: Download the PDF files for reference.     

Madras University question papers offer insight into the topics covered in the examination syllabus. They provide an overview of the significance of each chapter, highlighting that not all topics hold equal importance. Additionally, they help students understand the allocation of total marks for the examination. Following are some of the advantages of leveraging the Madras University question papers:

• Integral Role in Preparation: Madras University Question Papers play a pivotal role in a student's exam preparation process, providing valuable insight into the exam pattern and question types.
• Essential for Exam Readiness: Accessing specific old question papers online is crucial for students to adequately prepare for upcoming exams, ensuring they are familiar with the format and style of questions.
• Likelihood of Repetition: Questions from Madras University's previous year papers often reappear in examinations, making daily practice and solving previous year's papers a valuable habit for students seeking high scores.
• Effective Study Strategy: Regular practice with the previous year's question papers increases students' familiarity with the exam format and enhances their ability to tackle questions effectively during the actual exam.
• Deeper Topic Familiarity: Reviewing the University of Madras's previous year's question papers from the last five years offers students a deeper understanding of essential topics across chapters and subjects.
• Effective Revision: By revisiting the previous year's question papers, students can identify key areas of focus for revision, allowing them to strengthen their grasp on fundamental concepts before the exam.
• Success in Exams: Scoring well in exams requires students to put in extra effort, including gathering sample question papers and diligently practicing them to improve their performance.
• Effective Preparation Strategy: Practicing with a variety of question papers enables students to develop effective exam strategies, ultimately leading to improved performance and higher scores.

Madras University question papers serve as a crucial resource for students preparing for their semesters.  These papers offer invaluable insights into exam patterns and key focus areas, significantly enhancing exam readiness. Accessible in PDF format through the university's official website and conveniently provided in this article, they serve as essential resources for students striving for academic excellence. This article aims to facilitate easy access to these invaluable question papers, emphasizing the benefits of regular practice and preparation with them. Related Links:

We hope the above article helped provide insights into the Madras University question papers. For any further queries, feel free to post your questions in our CollegeDekho QnA section or call us at 1800-572-9877.

Are you feeling lost and unsure about what career path to take after completing 12th standard?

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Yes, the University of Madras releases question papers for students on the official website. Candidates can visit the official website and find the required question papers by entering the code for the concerned subject(s).

No, logging in is not required to access Madras University question paper PDFss. However, students need to know the subject name or subject code to obtain the same.

Yes, the University will release Madras University Question Papers for every subject and course separately. There will be sets of separate question papers for each subject as per the courses offered at the university.

It is important for a student to refer to Madras University previous year question papers for the following reasons:

• Helps students understand the syllabus.
• Alleviates exam anxiety and improves performance.
• Teaches time management by understanding the weightage of each section.

Students can download Madras University previous year question papers from the official website at unom.ac.in. by following the steps below:

• Open the official website of Madras University.
• Click on the "Examinations" tab.
• Select "Previous Question Papers" 
• Enter the subject code and click on the search button.
• A list of Madras University previous question papers, categorized by subject, will appear.
• Download the question papers PDF corresponding to the desired course or subject.

Yes, Madras University question papers are available for all courses, including undergraduate, postgraduate, and distance education programs.

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Thursday, June 23, 2022

University of madras cdz4a elements of operational research november 2019 question paper.

Madras University

NOVEMBER 2019

Question Paper Code: 62413

Subject code: MBT4A / CDG2A / CPM2B / CDC4A / CDZ4A

Subject: Elements of Operational Research

Course: B.Com II Year

04th Semester

Time : Three hours 

Maximum : 75 marks

.... Full question paper can be downloaded below.

Attachment in PDF :  Click here to download University of Madras CDZ4A Elements of Operational Research November 2019 Question Paper

Attachment in Scanned Copies:

B.E Civil Engineer Graduated from Government College of Engineering Tirunelveli in the year 2016. She has developed this website for the welfare of students community not only for students under Anna University Chennai, but for all universities located in India. That's why her website is named as www.IndianUniversityQuestionPapers.com . If you don't find any study materials that you are looking for, you may intimate her through contact page of this website to know her so that it will be useful for providing them as early as possible. You can also share your own study materials and it can be published in this website after verification and reviewing. Thank you!

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University of Madras Old Question Papers PDF Free Download

Here you can find out University of Madras (UNOM) Solved Previous Year Question Paper & also you can download this Madras University (MU) Question Paper in PDF Format. If you are searching for University of Madras Previous Year/Old or Model Question Papers, Question Bank or Madras University Question Papers please follow our site to download more question papers in PDF format.

Madras University Old Exam Papers

University of madras ug, pg sample papers, university of madras previous year question papers, madras university model papers download course wise/branch wise, download last 5 year question paper of university of madras.

Students who are searching for Madras University old solved question papers and model papers with answers for University of Madras exams are available on our website. Candidates can visit our website daily for continuous updates regarding University of Madras previous year’s papers to help you prepare well for the Madras University exams.

The University of Madras Previous year’s questions papers can be accessed in the official website of University of Madras. These old question papers would be very beneficial to understand the exam pattern and format. It will give an idea of suggestive questions. It can be used to identify the recurring questions for the exam, which will bring better results. From the years 2020, 2021, 2022, 2023 we can provide the Madras University previous year questions.

• Download Madras University 2023 Question Paper – Click Here
• Download Madras University 2022 Question Paper – Click Here
• Download Madras University 2021 Question Paper – Click Here
• Download Madras University 2020 Question Paper – Click Here
• Download Madras University 2019 Question Paper – Click Here

Hope this article helps the students to find sample/previous question papers. If you want more information regarding anything please visit official website of University of Madras.

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TYBMS Semester 6 Operation Research (Q.P. April 2019 with Solution)

 paper/ subject code 86001/ operation research, tybms semester 6 operation research , (q.p. april 2019 with solution), 1) april 2019 q.p. with   solution (pdf) , 2) november 2019 q.p. with  solution (pdf), 4 ) april 2023 q.p. with  solution (pdf).

Please check whether you have got the right question paper.

1. All questions are compulsory. (Subject to Internal Choice)

2. Figures to the right indicate full marks

3. Use of non-programmable calculator is allowed and mobile phones are not allowed.

4. Normal distribution table is printed on the last page for reference. Support your answers with diagrams / illustrations, wherever necessary

6. Graph papers will be supplied on request.

___________________________________________________________________________

Q1.A) Multiple choice questions (Attempt Any 8)                                                  (8)

I) ln linear programming, unbounded solution means ____________. .

a) infeasible solution   b) Degenerate solution

c) Infinite solutions     d) Unique solution

  Ans:  c) Infinite solutions

Ii) if m + n-1 = number of allocations in transportation, it means _________..

(Where 'M' is number of rows and N' is number of columns)

a) There is no degeneracy       b) Problem is unbalanced

c) Problem is degenerate        d) Solution is optimal

 Ans:  a) There is no degeneracy   

Ijü) floats for critical activities will be always _________________..

a) One             b) Zero

c) Highest        d) Same ás duration of the activity

 Ans:  b) Zero

Iv) the total time required to complete all the jobs-in a job sequencing problem is known as __________,.

a) Idle time                                 b) Processing time

c)Elapsed time                        d) Processing order

 Ans:  c)Elapsed time

V) in linear programming, _____________ represents mathematical equation of the limitations imposed by the problem..

a) Objective function              b) Decision variable

c)Redundancy                         d) Constraints

Ans:    d) Constraints

Vi) if in an assignment problem, number of rows is not equal to number of columns then ____________..

a) Problem is degenerate                                    b) Problem is ‘unbalanced

c) It is a maximization problem                      d) Optimal solution is not possible

Ans:    b ) Problem is ‘unbalanced

 vii) the maximum time in which an activity will be completed assuming all possible delays and postponements is termed as __________..

a) Optimistic time                   b) Most likely time

c) Pessimistic time                  d) Expected time

Ans:  c) Pessimistic time

Viii) the various alternatives or courses of actions available to each player in a game are called as __________..

a) Saddle points                      b) Strategies

c) Pay off                                d) 'n' player game

Ans:  b) Strategies

Ix) in simplex, a maximization problem is optimal when all delta j, i.e., cj-zj values are.

a) Either zero or positive                       b) Either zero or negative

c) Only positive                                  d) Only negative

Ans:     b) Either zero or negative

X) which of the following considers difference between two least costs for each row and column while finding initial basic feasible solution in transportation.

a) North west corner rule                    b) Least cost method

c) Vogel's Approximation method       d) Row minima method

Ans:    b) Least cost method

Q1.B) True or false (Attempt Any 7)                                               (7)

i) Probability of a project completing in its expected time (Te) will be always 100%

Ii) lf saddle point is available in a game, it is called as pure strategy game., iii) slack represents unutilized resources., iv) if in a transportation problem, number of rows is not equal to number of columns, then the problem is unbalanced., v) lf we introduce an unnecessary dummy activity, the error is termed as redundancy., vi) job sequencing problems are solved to ensure that, both, the total time to complete all jobs and idle time of each machine are maximum., vii) when more than one optimal solution is possible in a linear programming problem, it is termed as 'unique solution'., viii) regret matrix is made to convert a maximization problem into minimization problem in assignment., ix) critical path method (cpm) considers the three-time estimates: most likely, optimistic and pessimistic time estimates., x) in solving a job sequencing problem, it is assumed that all jobs require the same sequence of operations., q.2 a) a company produces 2 products a and b: x 1 and x 2 , are the quantities manufactured of products a and b respectively. the following objective function along with constraints is given to you: .

Max Z = 8x 1 + 16x 2 ,

Subject to constraints:

x 1 + x 2 < 200

x 2 < 125

x 1 + 2x 2 < 300

x 1 , x 2 > 0

Find how many units of Product A and Product B should be produced by the company so that the profit is maximized. Ls it a case of multiple optimal solutions? Use graphical method to solve the LPP.

Video solution.

x 1 + x 2 < 200   ---- (i)

x 2 < 125           ---- (ii)

x 1 + 2x 2 < 300 ---- (iii)

x 1 , x 2 > 0  

x 1 + x 2 = 200

Let X 1 = 0

0 + x 2 = 200

Therefore x 2 = 200                  (x 1 , x 2 ) = (0, 200)

Let X 2 = 0

 x 1 + 0 = 200

Therefore x 1 = 200                      (x 1 , x 2 ) = (200, 0)

  x 2 < 125    ---- (ii)

Let x 2 = 0

x 2 = 125                 (x 1 , x 2 ) = (0, 125)

x 1 + 2x 2 < 300     ---- (iii)

x 1 + 2x 2 = 300

Let x 1 = 0

 0 + 2x 2 = 300

            x 2 = 300 / 2                             Therefore x 2 = 150             (x 1 , x 2 ) = (0, 150)

x 1 + 2x 2 = 300 Let x 2 = 0 x 1 + 2(0) = 300 x 1 = 300                     (x 1 , x 2 ) = (300, 0)

Corner Point Method:

Optimal Profit Maximization is Rs. 2,400

Q2.b) you are given the per unit cost of transporting goods from 3 factories to 4 customers. the 3 factories a b and c have capacity to supply 500,300 and 200 units respectively. the 4 customers p, q, r and s require 180,150,350 and 320 units respectively., i) you are required to find the initial basic feasible solution using vogel's approximation method                                                                                                                 (5) ii) find the total cost of transportation schedule obtained using vam          (2).

Total Demand = 1000

Total Supply = 1000

Total Demand = Total Supply

Cost data is given

Minimization Problem

RIM Condition:

M + N – 1 = No. of Allocation

3 + 4 – 1 = 6

Therefore, RIM Condition is satisfied.

Optimal Solution is Non-Degeneracy

(ii) Total Cost of Transportation :

            = (150 x 10) + (230 x 12) + (120 x 13) + (180 x 7) + (120 x 8) + (200 x 7)

            = Rs. 9, 440

Q.2 C) You are given the following details for a project consisting of 8 activities:

(i) Draw the network diagram and identify the critical path.                    (3) (ii) Find earliest start time, earliest finish time, latest start time and latest finish time for each activity.                                                                                                      (4) (iii) Find free float for activity B.                                                              (1)

  Solution:    [Video Explanation ]

(i)                  Network Diagram

Paths in Network:

(1) A-E-F = 4 + 20 + 10 = 34 days

(2) A-D-G = 4 + 5 + 6 = 15 days

(3) B-G = 6 + 6 = 12 days

(4) C- H = 13 + 16 = 29

Projection Completion Time : 34 days

(ii)               Free Float for Activity B:

= Ej – Ei – t

= 9 – 0 – 6

= 15  

Q.2 D) There are 6 jobs to be performed in a factory and each would go through 2 machines A and B in the order AB. The processing time (in hours) is given for each job in each machine.

(i) determine the sequence of performing the jobs that would minimize the total time of completing all the jobs:                                                                                 (2) (ii) find the elapsed time.                                                                               (3) (iii) find idle time for both the machines.                                                    (2).

Solution :    [Video Explanation ]

(i)                  Optimal Sequence

A                                                                                                                           B

(ii)                 Elapsed Time Calculation :

  Total Min. Elapsed Time = 36 Hrs.

(iii)            Idle time for Machinery A    = 36 – 35 = 1 Hrs

Idle time for Machinery A    = 36 – 28 = 8 Hrs

Q.3. B) You are given the following details for a project with 8 activities.

(i) Draw the network diagram.                                                                                     (3)

(ii) Find the expected time of project completion along with standard deviation.       (2)

(iii) What is the probability of the project completing in 55 days?                               (2)

Ans:    [Video Explanation]

Network Diagram:

Paths in the Network:

1)       1-2-3-5-7-8  = 47 days

2)       1-2-4-6-7-8 = 33 days

Expected Project Completion Time : 47 days

Variance of critical path = 16/36 + 100/36 + 256/36 + 64/36 + 4/36 = 440/36 =12.22

SD of critical path = √variance

SD = √ 12.22   = 3.495                        = 3.5 days

Time = 55 days = te

Z = t – CP / SD

= 55 – 47 / 3.5 = 2.29 

Table value = 0.4890

P(55 days) = 0.5 + 0.4890      = 0.9890                      = 98.90% 

Q.3. C) You are given information about the cost (in Rs. Thousands) of performing different jobs by different persons. PI cannot perform J3. P3 cannot perform J4

(i)Obtain optimal assignmnt and find cost of such assignment.

(i)Is it a case of alternative optimal solution?

Ans:      [Video Explanation]

Prohibited Assignment = X (infinity)

The problem is unbalanced.

Taking P5 as Dummy

Cost is given.

Hence Minimization Problem.

Row Minimization

Column Minimization Not Required.

Min. No. of Lines = 4

Size of Matrix = 5 x 5

Therefore Not optimal

Change = Min. open Value = 4

Optimal Cost = 66,000

Q3.D) Two firms, Lacko textiles and Rayon textiles have 3 strategies each to select from. The 3 strategies are no advertisement, using moderate advertising and using heavy advertising. You are given the pay off matrix from view point of Lacko textiles, showing its market share under several combinations of strategies:

(    (i) Find the saddle point and value of game.      (ii) Comment on the strategy to be selected by both the companies.

Value of the Game = 50 x 10000 =     5,00,000

Q. 4 a) you are given a solution for a transportation cost problem. figures in each cell represent per unit transportation cost. figures in circle within each cell represent number of units allocated for transportation. x, y and z. are the 3 factories and a, b, c and d are the 4 customers..

(i) You are required to check the above solution for optimality.

(ii) If it is not optimal, use modified distribution method to obtain optimal solution.

(iii) Find optimal transportation cost.

Ans:  [Video Explanation]

No negative ∆, Hence Optimal Solution.

(iii) Optimal transportation Cost:

= (200 x 7) + (120 x 18) + (100 x 15) + (280 x 7) + (180 x 11) + (12 x 5)

= RS. 9,600

B) You are given the following information, for a project with 8 activities:

The cost of completing the eight activities in normal time is Rs.6,500.

Indirect cost is Rs 160 per day. The contract includes a penalty of Rs. 100 per day for every day of delay more than 17 days.

  (i)   Draw the network diagram and find critical path.

(i     (ii)  Crash the projèct duration to find the total 'cost of completing the project in 17 days (4)

  Ans:  [Video Explanation]

Q.4. C) A company produces 2 products x and xX) using three resources S1, S2 and S. Product x1 gives profit of Rs.30 per unit and product x2 gives profít of Rs.40 per unit. The 3 resources Si. S and S; are available to the extent of 200 units, 600 units and 500 units respectiveiy The following objective function and constraints are given to you:

Max Z = 30x1 + 40x2

Subject to constraints;

x 1 + 2x 2 < 200

8x 1 + 5x 2 < 600

3x 1 + 4x 2 < 500

X1 >0; x2 >0

You are given the following simplex solution to the above problem:

  A) With reference to the above table answer the following:

i) Check if the above solution is optimal or not.

ii) lf it is not optimal, find optimal solution.

B) With reference to the optimal simplex table in the above problem obtained by you, answer the following:

iii) Find the optimal product mix and optimal profit

iv) Which resources are scarce and which are, unutilized?

v) Is it a case of alternative solution? Justify your answer

vi) What are the shadow prices of the resources? Justify

Ans:       [Video Explanation]

Testing the given solution for optimality ;

Positive ∆

Hence, solution not optimal.

(ii) Revising the Solution for Optimality:

No positive ∆

Therefore, Optimal Solution

(iii) Optimal Product Mix;

No. of units of X1 = 200/11        = 18.18

No. of units of X1 = 1000/11      = 90.90

Optimal Profit:

Max Z = [30 x 200/11] + [40 x 1000/11]

          = Rs. 46,000 /11

          = Rs. 4,181.81

(iv) Abundant Resource:

S3 = 900/11 ----- in optimal solution

Therefore Unutilized Capacity of S3 = 900 / 11

S3 is Abundant resource.

S1 and S2 are non-basis variable in optimal solution.

 Unutilized Capacity of S1 and S2 are 0

(i)                 ∆ of non basis variable :

∆ of S1 = - 170 / 11

∆ of S2 = -20/11

No zero ∆ value.

Hence, this is a case of Unique Solution.

There is no alternate optimal solution.

(ii)              Zj value of slack variables:

Q.5 A) Explain the concepts : Total float, free float, Independent float and Interfering float.           (8) 

(a) Total float:

lt is the amount of time by which the completion of an activity can be delayed beyond the earliest possible finishing time without affecting total project completion time.

 Total Float = (LST - EST) or (LFT - EFT)

.:: Total float = LST - EST -[;-t]-E Total Float = [Lj- E -t

(b) Free float:  It is the amount of time by which the completion of an activity can be delayed beyond the earliest finishing time without affecting the earliest possible start of a subsequent activity.

Free float = Earliest starting time of subsequent activity - Earliest finishing time of activity ij = Ej- [E, + t;] . Free Float = Ej- E-tj

(c) Independent float:  It is the amount of time by which the start of an activity can be delayed without affecting the earliest start of a subsequent activity, assuming that the preceding activity has finished at its latest finishing time. .

:. Independent float = Earliest starting time of subsequent activity - Latest finishing time of preceding activity - ij

:. Independent Float = [Ej-Li]-tij;

(d) Interfering float:  It is that part of total float which reduces the float of a subsequent activity. It is the amount of time by which the earliest possible start of a subsequent activity will be delayed if activity ÷ finishes on latest finishing time.

:. Interfering float = Latest finishing time of activity ij - Earliest starting time of subsequent activity. :. Interfering Float= Lj-Ej

B) Discuss any 5 areas where techniques of operation Research can be applied.    (7) 

OR techniques are applied to a variety of business problems. Some examples are:

(A) Production management:

(1) To calculate loss of time due to waiting time, queuing time etc.

(2) To decide optimum allocation of jobs and optimum sequence in which jobs should be sequenced.

(B) Personnel management:

(1) To study labour turnover. (2) To do human resource planning. (3) To decide number of personnel required to be kept on standby in case of demand for higher manpower.

(C) Inventory management: (1) To study economic lot size to be ordered.

(D) Marketing management: (1) To decide optimal product mix for maximum profit. (2) Media selection for advertising for maximum reach. (3) Sales forecasting.

(E) Transportation management: (1) To determine transportation schedule for minimum cost or minimum time.

(F) Project management (1) To identify critical and non-critical activities of a project (2) To determine minimum project completion time. (3) To determine optimal project cost.

(G) Financial management: project. (1) To decide investment portfolio to maximize return on investment. of such nature that it is impossible to find a feasible solution that can satis1y a the constraints. 

c) Answer any 3 of the following :            (15) 

I) explain the terms: redundant constraints and infeasible solution in linear programming. .

Ans:  A redundant constraint is the one which does not affect the optimal solution. Even if that constraint is not considered, we can still obtain the solution to the problem. Since the constraint is not required for obtaining the optimal solution, it is called redundant constraint cost.

Following sketch explains redundancy (redundant constraint):

There is no common feasible region for line AB and line CD

Hence, solution is infeasible.

A redundarnt constraint is the one which does not affect the optimal solution. Even if that constraint is not considered, we can still obtain the solution to the problem. Since the constraint is not required for obtaining the optimal solution, it is called redundant constraint. cost.

The feasible region for the above problem is OABC. The 3rd constraint does not affect the feasible region. Hence, the constraint [X1 S 16] is redundant constraint.

ii) what do you means by alternative optimal solution in transportation? How do you find that alternative solution? 

Alternate optimal solution or multiple optimal solutions mean there are two sets of solutions which provide the same optimal cost or optimal profit:

(a) In the optimal solution to a transportation problem, if there is an empty cell with zero A value, it means there is alternate optimal solution.

(b) To find alternate optimal solution, we should construct a closed loop from the empty cell with zero A. The new table we obtain after looping is the alternate optimal solution.

iii) Explain the time coat trade off in project crashing. 

The execution of a project involves two types of costs, direct cost and indirect cost.

(a) Direct costs: These include costs of materials, machinery, tools, manhours etc. When we estimate the duration of various activities in the project, it is assumed that normal amount of labour (manhours) & machines will be required to complete these activities. The estimation of direct costs is done based on the normal amount of resource required. This estimation gives us minimum possible direct cost required to complete the project. When we want to complete the project in a shorter period than critical path, we will need to employ more resources. Hence, direct cost will increase.

(b) Indirect costs: These include rent, overheads, administrative costs etc. Indirect costs vary with time. They are expressed on per day (or per week etc.) basis. Hence, when we shorten the project completion time, total indirect cost reduces.

Total P'roject Cost = Direct Cost + Indirect Cost

iV) Discuss the signification of theory of game. Briefly discuss the terms. Player and pay off.

Ans: Every one business party. The situation (also called competitive situation) involves more parties involved could be corporate. individuals, small firms or A number of outcome alternatives are available to each party for decision making. The (i.e. profit or loss) of the business decision does not depend on the alternative selected by one party alone, but on the interaction between the decisions of all the parties involved in the situation. Each party will try to select the alternative which maximizes gains for it, at the cost of its competitors. "Games Theory" deals with such business situations or problems where multiple parties are involved in the conflict through interaction of their alternatives or decisions.

Players: The various participants or decision markers in the game are called "Players". A game must have minimum two players (or competitors). A game having two competitors opposing each other is called 'two person game' and a game having more than 2 players is called 'n-person game'.

Payoff: Payoff is the outcome of the interaction of selected strategies of opponents in the game. Positive payoff is gain and negative payoff is loss. In a 'two person game', when one party gains, the other party loses.

v) Distinguished between PERT and CPM. 

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