Programmers A B C D Solution:
|
|
- Samson Lamb
- 5 years ago
- Views:
Transcription
1 P a g e Q: A firm has normally distributed forecast of usage with MAD=0 units. It desires a service level, which limits the stock, out to one order cycle per year. Determine Standard Deviation (SD), if the order quantity is normally a week`s supply. Solution: SD (0) SD SD 3.4 (0). (0) SD (.)(0) SD 6.64 Q: A company centre has got four experts programmers. The centre needs four application programmers to be developed. The head of the computer centre, after studying carefully the programmer s to be developed, estimate the computer time in minutes required by the respective experts to develop the application programmers as follows. Programmers A B C D Solution: Programmers A B C D Programmers A B C D x x 4 0x 0 0x 0 Q: the cost of a new machine is Rs The maintenance cost during the nth year is given by M n = Rs.00 (n-), where n=,, 3 If the discount rate per year is 0.0, determine discount factor (v n- ) for each year.
2 P a g e Solution: M = 000 M n = 00 (n-) V = 0.0 (v n- ) =? Nth year M n (v n- ) Or Nth year (v n- ) Q: Determine whether the following Transportation model has initial feasible solution? D D D 3 D 4 Supple Q x x x 3 x 4 6 Q X X X 3 X 4 8 Q 3 X 3 X 3 X 33 X 34 0 Demand Solution: The transportation problems can be represented mathematically as a linear programming model. The Objective function in this problem is to minimize the total transportation cost given by Z = c x + c x c mnx mn Subject to the restrictions: Row restrictions: x + x + x 3 + x 4 = 6 x + x + x 3 + x 4 = 8
3 P a g e 3 x 3 + x 3 + x 33 + x 34 = 0 Column restrictions: x + x + x 3 + x 4 = 4 x + x + x 3 + x 4 = 6 x 3 + x 3 + x 33 + x 43 = 8 x 4 + x 4 + x 34 + x 44 = 6 And x + x + x 3 + x 4 0 It should be noted that the model has feasible solutions only if a + a + a 3 + a 4 = Or m n i=0 a i = b j j= Q: Salesman Region A B C D E F Do next step by applying Hungarian method? Solution: Salesman Region A 0x 0x 0x B 0 0 0x 30 4 C D E F
4 P a g e 4 Here we have only three assignments. But we must have four assignments. With this maximal assignment we have to draw the minimum number of lines to cover all the zeros. Q: An oil company has 8 unit of money available for exploration of three sites. If oil is present at a site, the probability of finding it depends upon the amount allocated for exploiting the site as given below Site I Site II Site III The probability that the oil exits at sites I, II and III is 0.4, 0.3 and 0. respectively; we have to find the optimal allocating of money. Stage I is given below, only do stage it. Stage I Max. Z=0.4P (x ) + 0.3P (x ) Subject to: x +x +x 8 No. of boxes x f (x ) Q. a person wants to decide the constituents of a diet which will fulfill his daily requirements of protein, fats and carbohydrates at the minimum cost. The choice is to be made from four different types of foods. The yields per unit of these foods are given in the table below: Food type Yield per unit Proteins Fats carbohydrates Cost per unit (Rs.) Min Requirement Solution:
5 P a g e Let x, x, x3 and x4 denote the number of units of food of type,, 3 & 4 respectively. Objective is to minimize the cost i.e. Minimize Z = 4x+40x+8x3+6x4 Constraints are on the fulfillment of the daily requirements of various constituents i.e. Proteins - 3x + 4x + 8x3 + 6x4 800 Fats - x + x + x3 + x4 00, Carbohydrates - 6x + 4x + x3 + 4x4 00. Where x, x, x3, x4 each 0 Question No: 4 ( Marks: ) Fall 0 A branch of Punjab National Bank has only one typist. Since the typing work varies in length (number of pages to be typed), the typing rate is randomly distributed approximating a Poisson distribution with mean service rate of 8 letters per hour. The letters arrive at a rate of per hour during the entire 8 hour worki9ng day. If the typewriter is valued at Rs..0 per hour, Determine Average system time. : W s= /µ-λ = /8- =/3hr=/3*60=0 min Question No: 4 ( Marks: ) An oil company has 8 unit of money available for exploration of three sites. If oil is present at a site, the probability of finding it depends upon the amount allocated for exploiting the site as given below:
6 P a g e Site I Site II Site III The probability that the oil exits at sites I, II and III is 0.4, 0.3 and 0. respectively; we have to find the optimal allocating of money. Do stage I only. Not Attempted Question No: 43 ( Marks: ) Write the relationship between the activities.
7 P a g e X approches to Y X also approches to Z Y approches to Z Whether A and b might have the values between the centre points Question No: 44 ( Marks: ) For the mathematical form of a Transportation problem (T.P) i m j n min z c x () i j ij ij subject to j n j i m i x a (), i,,, m(sources) ij i x b (3), i,,, n(destinations) ij j Describe the practical significance of all the above equations(), () and (3). :
8 P a g e 8 The above is a mathematical formulation of a transportation problem and we can adopt the linear programming technique with equality constraints. Here the algebraic procedure of the simple method may not be the best method to solve the problem and hence more efficient and simpler streamlined procedures have been developed to solve transportation problems. Question No: 4 ( Marks: 3 ) The milk plant at a city distributes its products by trucks, located at the loading dock. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver that is only waiting. The company has asked the milk plant management either to go in for a second loading dock or discount prices equivalent to the waiting time, the following data available Average arrival rate 3 per hour Average service rate 4 per hour The transport company has provided 40%of the total number of trucks. Assuming that these rates are random according to Poisson distribution, determine a) The probability that a truck has to wait. b) The waiting time of a truck that waits. The probability that a truck has to wait The waiting time of a truck that waits.
9 P a g e 9 round about 40 minutes of each truck. Question No: 46 ( Marks: 3 ) A company has a machine whose cost is Rs. 30,000. Its maintenance cost and resale value at the end of different years are as given below: Years Maintenance Cost Resale Value Determine capital cost for each year. Question No: 4 ( Marks: 3 ) A firm produced three products. These products are processed on three different machines. The time required to manufacturer one unit of each of the three products and the daily capacities of the three machines are given in the table: Machines Time per unit (minutes) Product Product Product 3 Machine Capacity (minutes / day) M M M
10 P a g e 0 It is required to determine the daily number of units to be manufactured for each product. The profit per unit for product, and 3 is Rs. 4, Rs. 3 and Rs. 6 respectively. It is assumed that all the amounts produced are consumed in the market. Write the constraints of above Linear Programming Problem. Step Find the key decision to be made. The key decision is to decide the extent of product,&3 to be produced as this can vary. Step Assume symbols for the extent of production. Let the extent of Product,&3 be X, X & X3. Step 3 Express the feasible alternatives mathematically in terms of variables. Feasible alternatives are those which are physically, economically and financially possible. In this example, feasible alternatives are sets of values of x, x & x3, where x,x &x3 0 since negative production has no meaning and is not feasible. Step 4 Mention the object quantitatively and express it as a linear function of variables. IN the present example, objective is to maximize the profit. i.e. Maximize Z = 4x+3x+6x3 Step Express the constraints as linear equations/inequalities in terms of variables. Here, constraints are o the machine capacities and can be mathematically expressed as x + 3x + x3 440, 4x + 0x + 3x3 40, x + x + 0x Question No: 48 ( Marks: 3 ) Express the following Transportation problem (T.P) table into algebraic form with proper objective function and non-negative constraints
11 P a g e D D D 3 Supply O c c c 3 O c O 3 c 3 Deman d c c 3 c 3 c x S D S 6y D 3 S S 8z 0 Question No: 49 ( Marks: ) 3 Supply Deman d Complete the above transportation Model by Vogel Approximation Method. And also find the starting basic feasible solution.
12 P a g e 3 Supply Deman d Cost = + + (6) + + () = This is the initial basic solution consider u = and v = and v = 3 Question No: 0 ( Marks: ) Check whether the given initial basic feasible solution is optimal or not
13 P a g e 3 3 Supply Deman d Cost = + + (6) + + () = This is the initial basic solution consider u = and v = and v = 3 it is a n optimal solution according to if we put formula Question No: ( Marks: ) A company cost Rs. 00 operations and maintenance costs are zero for the first year and increased by Rs. 00 every year. If money is worth % every year, calculate present worth (P(r)) for each year. The resale value of the machine is negligibly small.
14 P a g e 4 for each year increase in money = % means to say that company significes 0 ruppes every year the company capital must be increaing as 0 * 00 Question No: ( Marks: ) Express the following linear programming problem in standard form and also construct its initial simplex table. Max Z = 3x+y Subject to constraints: x + y 4 x y x,y 0 Blank Data marks qs Mth60 30 July 03 final term paper: Q: ek bohat sari activities wali diagram di hui thi or qs ye tha
15 P a g e Find EFT for each activity? Q: To find optimality condition we use UV multiplier process Find a) U+V b) U3+V3 Q: 3 ya mark ka tha ye qs Contractor side wali values yad nai Building: Contractor: A B C D Operate first step by optimizing row wise the above assignment model. Q: state principal of optimality (optimal policy) for dynamic programming? Q: fin EST and EFT for each activity. A B 8 6 D 0 C 0 E 4
16 P a g e 6 3 Q: marks Find a) P3 b) P3 Using Pij= Ui + Vj Cij suppose U = 0 and U = Q: ek statement thi us me se Average Queuing length find krna thi. Q: Minimizing setup times, which are given? ( marks) Job ki values yad nai Job Job Job3 Job4 Machine 4 Machine Machine 3 Machine 4 Q: ek mark ka qs itna long tha k word pe paste krne se ek se zyada page ki just statement thi. Replacement Of Items with change in value and time
17 P a g e It is assumed that the maintenance cost increases with time and each cost is to be paid just in the start of the period. Let the money carry a rate of interest r per year. Thus a rupee invested now will be worth ( + r) after a year, (+r) after two years and so on. Do first step? No. of stores 3 No. of boxes No. of stores 3 No. of boxes Diff b/w pert n CPM?? PERT (Programme Evaluation & Review Technique) is event oriented whereas CPM (Critical Path Method) is activity oriented. In CPM based network analysis no allowance is made for the uncertainties in the duration of time involved. In CPM, times are related to costs Q: Make two steps, of rows and columns of the following table
18 P a g e 8 : Least ko sab me se Minus krna hay pehlay rows, then columns, to have atleast one zero in all. Markets / salesmen I II III IV A B C D Markets / salesmen I II III IV A B C D Complete the table By VOgha s method:
19 P a g e 9 Sol: Red is solved one 3 Supply Demand 0 6 july 03. a branch of bank has only one typist. typing rate is randomly distributed approximating a Poisson distribution with mean service rate of 8/hour. Letter arrive rate is /hour during the entire 8 hour working day if writer is value.0 per hour determine the equipment utilization? marks and same this question is appeared as marks question. Scenario was given and we have to tell the objective function of linear programming... marks 3. Table was given n determine that transportation model has initial feasible solution... marks 4. State principle of optimality for dynamic programming... marks. Transportation model was given and one block has x we have to find the value of x... 3 marks 6. Values were given and we need to tell the capital cost for each year... 3 marks. In the context of pert and CPM summarize the project planning techniques 8. One stage problem is given find the two stage problem s Fi*(s) Xi Table was given and asked that check initial solution is feasible or not... marks 0. Question no was again appeared as marks question. The cost of the new machine is 000. Maintenance during the nth year is given by Mn = 00 rps (n-) when n =,, 3...if discount rate per year is 0.0 calculate the present worth... marks. Graph was given and question was construct the table relation show between events and activities. mark s
ST. JOSEPH S COLLEGE OF ARTS & SCIENCE (AUTONOMOUS) CUDDALORE-1
ST. JOSEPH S COLLEGE OF ARTS & SCIENCE (AUTONOMOUS) CUDDALORE-1 SUB:OPERATION RESEARCH CLASS: III B.SC SUB CODE:EMT617S SUB INCHARGE:S.JOHNSON SAVARIMUTHU 2 MARKS QUESTIONS 1. Write the general model of
More informationTransportation Problem
Transportation Problem. Production costs at factories F, F, F and F 4 are Rs.,, and respectively. The production capacities are 0, 70, 40 and 0 units respectively. Four stores S, S, S and S 4 have requirements
More information2. Linear Programming Problem
. Linear Programming Problem. Introduction to Linear Programming Problem (LPP). When to apply LPP or Requirement for a LPP.3 General form of LPP. Assumptions in LPP. Applications of Linear Programming.6
More informationThe Transportation Problem
CHAPTER 12 The Transportation Problem Basic Concepts 1. Transportation Problem: BASIC CONCEPTS AND FORMULA This type of problem deals with optimization of transportation cost in a distribution scenario
More informationBachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.)
AOR-01 ASSIGNMENT BOOKLET Bachelor s Degree Programme Operations Research (Valid from 1st January, 2012 to 30th November, 2012.) It is compulsory to submit the assignment before filling in the exam form.
More informationOperations Research: Introduction. Concept of a Model
Origin and Development Features Operations Research: Introduction Term or coined in 1940 by Meclosky & Trefthan in U.K. came into existence during World War II for military projects for solving strategic
More informationLINEAR PROGRAMMING MODULE Part 1 - Model Formulation INTRODUCTION
Name: LINEAR PROGRAMMING MODULE Part 1 - Model Formulation INTRODUCTION In general, a mathematical model is either deterministic or probabilistic. For example, the models and algorithms shown in the Graph-Optimization
More informationThe Assignment Problem
CHAPTER 12 The Assignment Problem Basic Concepts Assignment Algorithm The Assignment Problem is another special case of LPP. It occurs when m jobs are to be assigned to n facilities on a one-to-one basis
More informationConcept and Definition. Characteristics of OR (Features) Phases of OR
Concept and Definition Operations research signifies research on operations. It is the organized application of modern science, mathematics and computer techniques to complex military, government, business
More informationSyllabus, Question Paper, Programs of BCA, BBA
KA-3506 First Year B. B. A. (Sem. I) (CBCS) Examination O ctober / N ovem ber - 2012 Quantitative Method - I (Mathematics Oriented) Time : Hours] Instructions : (1) ssuqih C t$unki«(l f e w i (3t u «.»A
More informationStudy Unit 3 : Linear algebra
1 Study Unit 3 : Linear algebra Chapter 3 : Sections 3.1, 3.2.1, 3.2.5, 3.3 Study guide C.2, C.3 and C.4 Chapter 9 : Section 9.1 1. Two equations in two unknowns Algebraically Method 1: Elimination Step
More informationFormulating and Solving a Linear Programming Model for Product- Mix Linear Problems with n Products
Formulating and Solving a Linear Programming Model for Product- Mix Linear Problems with n Products Berhe Zewde Aregawi Head, Quality Assurance of College of Natural and Computational Sciences Department
More informationDecision Mathematics D2 Advanced/Advanced Subsidiary. Monday 1 June 2009 Morning Time: 1 hour 30 minutes
Paper Reference(s) 6690/01 Edexcel GCE Decision Mathematics D2 Advanced/Advanced Subsidiary Monday 1 June 2009 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included with
More informationThe TransPacific agreement A good thing for VietNam?
The TransPacific agreement A good thing for VietNam? Jean Louis Brillet, France For presentation at the LINK 2014 Conference New York, 22nd 24th October, 2014 Advertisement!!! The model uses EViews The
More informationDuality in LPP Every LPP called the primal is associated with another LPP called dual. Either of the problems is primal with the other one as dual. The optimal solution of either problem reveals the information
More informationASSIGNMENT - 1 M.Sc. DEGREE EXAMINATION, MAY 2019 Second Year STATISTICS. Statistical Quality Control MAXIMUM : 30 MARKS ANSWER ALL QUESTIONS
ASSIGNMENT - 1 Statistical Quality Control (DMSTT21) Q1) a) Explain the role and importance of statistical quality control in industry. b) Explain control charts for variables. Write the LCL, UCL for X,
More informationMULTIPLE CHOICE QUESTIONS DECISION SCIENCE
MULTIPLE CHOICE QUESTIONS DECISION SCIENCE 1. Decision Science approach is a. Multi-disciplinary b. Scientific c. Intuitive 2. For analyzing a problem, decision-makers should study a. Its qualitative aspects
More informationPROJECT MANAGEMENT CHAPTER 1
PROJECT MANAGEMENT CHAPTER 1 Project management is the process and activity of planning, organizing, motivating, and controlling resources, procedures and protocols to achieve specific goals in scientific
More informationPREPARED BY: INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 PREPARED BY: A. SOMAIAH, ASST. PROFESSOR T. VANAJA, ASST. PROFESSOR DEPT. OF MECHANICAL ENGINEERING 1 Syllabus UNIT-I Development
More informationCHAPTER 11 Integer Programming, Goal Programming, and Nonlinear Programming
Integer Programming, Goal Programming, and Nonlinear Programming CHAPTER 11 253 CHAPTER 11 Integer Programming, Goal Programming, and Nonlinear Programming TRUE/FALSE 11.1 If conditions require that all
More informationPractice Questions for Math 131 Exam # 1
Practice Questions for Math 131 Exam # 1 1) A company produces a product for which the variable cost per unit is $3.50 and fixed cost 1) is $20,000 per year. Next year, the company wants the total cost
More informationExample: 1. In this chapter we will discuss the transportation and assignment problems which are two special kinds of linear programming.
Ch. 4 THE TRANSPORTATION AND ASSIGNMENT PROBLEMS In this chapter we will discuss the transportation and assignment problems which are two special kinds of linear programming. deals with transporting goods
More informationII BSc(Information Technology)-[ ] Semester-III Allied:Computer Based Optimization Techniques-312C Multiple Choice Questions.
Dr.G.R.Damodaran College of Science (Autonomous, affiliated to the Bharathiar University, recognized by the UGC)Re-accredited at the 'A' Grade Level by the NAAC and ISO 9001:2008 Certified CRISL rated
More informationUNIT 4 TRANSPORTATION PROBLEM
UNIT 4 TRANSPORTATION PROLEM Structure 4.1 Introduction Objectives 4.2 Mathematical Formulation of the Transportation Problem 4.3 Methods of Finding Initial asic Feasible Solution North-West orner Rule
More information56:171 Operations Research Fall 1998
56:171 Operations Research Fall 1998 Quiz Solutions D.L.Bricker Dept of Mechanical & Industrial Engineering University of Iowa 56:171 Operations Research Quiz
More informationEconomics 203: Intermediate Microeconomics. Calculus Review. A function f, is a rule assigning a value y for each value x.
Economics 203: Intermediate Microeconomics Calculus Review Functions, Graphs and Coordinates Econ 203 Calculus Review p. 1 Functions: A function f, is a rule assigning a value y for each value x. The following
More informationQuestions and solutions operational research (OR)
MCM20 6/30/06 5:40 PM Page 561 20 Questions and solutions operational research (OR) Summary The Operational Research Society explains OR as development of a scientific model of a system incorporating measurements
More informationSection 4.1 Solving Systems of Linear Inequalities
Section 4.1 Solving Systems of Linear Inequalities Question 1 How do you graph a linear inequality? Question 2 How do you graph a system of linear inequalities? Question 1 How do you graph a linear inequality?
More information...(iii), x 2 Example 7: Geetha Perfume Company produces both perfumes and body spray from two flower extracts F 1. The following data is provided:
The LP formulation is Linear Programming: Graphical Method Maximize, Z = 2x + 7x 2 Subject to constraints, 2x + x 2 200...(i) x 75...(ii) x 2 00...(iii) where x, x 2 ³ 0 Example 7: Geetha Perfume Company
More informationThe Transportation Problem
11 The Transportation Problem Question 1 The initial allocation of a transportation problem, alongwith the unit cost of transportation from each origin to destination is given below. You are required to
More informationDEPARTMENT OF MATHEMATICS
This is for your practice. DEPARTMENT OF MATHEMATICS Ma162 Samples from old Final Exams 1. Fred Foy has $100, 000 to invest in stocks, bonds and a money market account. The stocks have an expected return
More informationRECURSION EQUATION FOR
Math 46 Lecture 8 Infinite Horizon discounted reward problem From the last lecture: The value function of policy u for the infinite horizon problem with discount factor a and initial state i is W i, u
More informationORI 390Q Models and Analysis of Manufacturing Systems First Exam, fall 1994
ORI 90Q Models and Analysis of Manufacturing Systems First Exam, fall 1994 (time, defect rate) (12,0.05) 5 6 V A (16,0.07) (15,0.07) (5,0) M 1 1 2 M1 M2 O A (10,0.1) 7 8 V B (8,0.2) M4 2 4 M5 The figure
More informationSEXTANT & SEXTANT PE frequently asked questions
SEXTANT & SEXTANT PE frequently asked questions What is SEXTANT? SEXTANT is a software application that helps Financial Executives and Estimators determine their costing and budgeting standards also known
More information2 Functions and Their
CHAPTER Functions and Their Applications Chapter Outline Introduction The Concept of a Function Types of Functions Roots (Zeros) of a Function Some Useful Functions in Business and Economics Equilibrium
More informationDr. S. Bourazza Math-473 Jazan University Department of Mathematics
Dr. Said Bourazza Department of Mathematics Jazan University 1 P a g e Contents: Chapter 0: Modelization 3 Chapter1: Graphical Methods 7 Chapter2: Simplex method 13 Chapter3: Duality 36 Chapter4: Transportation
More informationMath 141:512. Practice Exam 1 (extra credit) Due: February 6, 2019
Math 141:512 Due: February 6, 2019 Practice Exam 1 (extra credit) This is an open book, extra credit practice exam which covers the material that Exam 1 will cover (Sections 1.3, 1.4, 2.1, 2.2, 2.3, 2.4,
More informationMSA 640 Homework #2 Due September 17, points total / 20 points per question Show all work leading to your answers
Name MSA 640 Homework #2 Due September 17, 2010 100 points total / 20 points per question Show all work leading to your answers 1. The annual demand for a particular type of valve is 3,500 units. The cost
More informationTest 2 VERSION A STAT 3090 Fall 2017
Multiple Choice: (Questions 1 20) Answer the following questions on the scantron provided using a #2 pencil. Bubble the response that best answers the question. Each multiple choice correct response is
More information56:171 Operations Research Midterm Exam - October 26, 1989 Instructor: D.L. Bricker
56:171 Operations Research Midterm Exam - October 26, 1989 Instructor: D.L. Bricker Answer all of Part One and two (of the four) problems of Part Two Problem: 1 2 3 4 5 6 7 8 TOTAL Possible: 16 12 20 10
More informationCMA Students Newsletter (For Intermediate Students)
Special Edition on Assignment Problem An assignment problem is a special case of transportation problem, where the objective is to assign a number of resources to an equal number of activities so as to
More informationMA 162: Finite Mathematics - Section 3.3/4.1
MA 162: Finite Mathematics - Section 3.3/4.1 Fall 2014 Ray Kremer University of Kentucky October 6, 2014 Announcements: Homework 3.3 due Tuesday at 6pm. Homework 4.1 due Friday at 6pm. Exam scores were
More informationChapter 4. Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall 4-1
Linear Programming: Modeling Examples Chapter 4 4-1 Chapter Topics A Product Mix Example A Diet Example An Investment Example A Marketing Example A Transportation Example A Blend Example A Multiperiod
More informationSocial Science/Commerce Calculus I: Assignment #10 - Solutions Page 1/15
Social Science/Commerce Calculus I: Assignment #10 - Solutions Page 1/15 1. Consider the function f (x) = x - 8x + 3, on the interval 0 x 8. The global (absolute) maximum of f (x) (on the given interval)
More informationW P 1 30 / 10 / P 2 25 / 15 / P 3 20 / / 0 20 / 10 / 0 35 / 20 / 0
11 P 1 and W 1 with shipping cost. The column total (i.e. market requirement) corresponding to this cell is 2 while the row total (Plant capacity) is. So we allocate 2 units to this cell. Not the market
More informationOptimization Methods in Management Science
Problem Set Rules: Optimization Methods in Management Science MIT 15.053, Spring 2013 Problem Set 1 (Second Group of Students) Students with first letter of surnames G Z Due: February 12, 2013 1. Each
More informationDuration of online examination will be of 1 Hour 20 minutes (80 minutes).
Program Name: SC Subject: Production and Operations Management Assessment Name: POM - Exam Weightage: 70 Total Marks: 70 Duration: 80 mins Online Examination: Online examination is a Computer based examination.
More informationCOT 6936: Topics in Algorithms! Giri Narasimhan. ECS 254A / EC 2443; Phone: x3748
COT 6936: Topics in Algorithms! Giri Narasimhan ECS 254A / EC 2443; Phone: x3748 giri@cs.fiu.edu https://moodle.cis.fiu.edu/v2.1/course/view.php?id=612 Gaussian Elimination! Solving a system of simultaneous
More informationOptimization Prof. A. Goswami Department of Mathematics Indian Institute of Technology, Kharagpur. Lecture - 20 Travelling Salesman Problem
Optimization Prof. A. Goswami Department of Mathematics Indian Institute of Technology, Kharagpur Lecture - 20 Travelling Salesman Problem Today we are going to discuss the travelling salesman problem.
More informationPlanning and Scheduling of batch processes. Prof. Cesar de Prada ISA-UVA
Planning and Scheduling of batch processes Prof. Cesar de Prada ISA-UVA prada@autom.uva.es Outline Batch processes and batch plants Basic concepts of scheduling How to formulate scheduling problems Solution
More information56:171 Operations Research Final Examination December 15, 1998
56:171 Operations Research Final Examination December 15, 1998 Write your name on the first page, and initial the other pages. Answer both Parts A and B, and 4 (out of 5) problems from Part C. Possible
More informationSYMBIOSIS CENTRE FOR DISTANCE LEARNING (SCDL) Subject: production and operations management
Sample Questions: Section I: Subjective Questions 1. What are the inputs required to plan a master production schedule? 2. What are the different operations schedule types based on time and applications?
More informationLinear Programming Applications. Transportation Problem
Linear Programming Applications Transportation Problem 1 Introduction Transportation problem is a special problem of its own structure. Planning model that allocates resources, machines, materials, capital
More informationDeterministic Operations Research, ME 366Q and ORI 391 Chapter 2: Homework #2 Solutions
Deterministic Operations Research, ME 366Q and ORI 391 Chapter 2: Homework #2 Solutions 11. Consider the following linear program. Maximize z = 6x 1 + 3x 2 subject to x 1 + 2x 2 2x 1 + x 2 20 x 1 x 2 x
More informationLecture Notes for January 23, 2012: Existence of general equilibrium in an economy with an excess demand function
Lecture Notes for January 23, 2012: Existence of general equilibrium in an economy with an excess demand function The plan of the course for the next month is to create a model of a competitive economy
More informationLinear programming: introduction and examples
Linear programming: introduction and examples G. Ferrari Trecate Dipartimento di Ingegneria Industriale e dell Informazione Università degli Studi di Pavia Industrial Automation Ferrari Trecate (DIS) Linear
More informationGenetic Algorithm. Outline
Genetic Algorithm 056: 166 Production Systems Shital Shah SPRING 2004 Outline Genetic Algorithm (GA) Applications Search space Step-by-step GA Mechanism Examples GA performance Other GA examples 1 Genetic
More informationMS-E2140. Lecture 1. (course book chapters )
Linear Programming MS-E2140 Motivations and background Lecture 1 (course book chapters 1.1-1.4) Linear programming problems and examples Problem manipulations and standard form problems Graphical representation
More informationBusiness Mathematics and Statistics (MATH0203) Chapter 1: Correlation & Regression
Business Mathematics and Statistics (MATH0203) Chapter 1: Correlation & Regression Dependent and independent variables The independent variable (x) is the one that is chosen freely or occur naturally.
More information42 Average risk. Profit = (8 5)x 1 é ù. + (14 10)x 3
CHAPTER 2 1. Let x 1 and x 2 be the output of P and V respectively. The LPP is: Maximise Z = 40x 1 + 30x 2 Profit Subject to 400x 1 + 350x 2 250,000 Steel 85x 1 + 50x 2 26,100 Lathe 55x 1 + 30x 2 43,500
More informationM.SC. MATHEMATICS - II YEAR
MANONMANIAM SUNDARANAR UNIVERSITY DIRECTORATE OF DISTANCE & CONTINUING EDUCATION TIRUNELVELI 627012, TAMIL NADU M.SC. MATHEMATICS - II YEAR DKM24 - OPERATIONS RESEARCH (From the academic year 2016-17)
More informationFundamentals of Operations Research. Prof. G. Srinivasan. Indian Institute of Technology Madras. Lecture No. # 15
Fundamentals of Operations Research Prof. G. Srinivasan Indian Institute of Technology Madras Lecture No. # 15 Transportation Problem - Other Issues Assignment Problem - Introduction In the last lecture
More informationSpring 2018 IE 102. Operations Research and Mathematical Programming Part 2
Spring 2018 IE 102 Operations Research and Mathematical Programming Part 2 Graphical Solution of 2-variable LP Problems Consider an example max x 1 + 3 x 2 s.t. x 1 + x 2 6 (1) - x 1 + 2x 2 8 (2) x 1,
More informationLinear Programming. H. R. Alvarez A., Ph. D. 1
Linear Programming H. R. Alvarez A., Ph. D. 1 Introduction It is a mathematical technique that allows the selection of the best course of action defining a program of feasible actions. The objective of
More informationLooking Ahead to Chapter 4
Looking Ahead to Chapter Focus In Chapter, you will learn about functions and function notation, and you will find the domain and range of a function. You will also learn about real numbers and their properties,
More informationREVIEW: HSPA Skills 2 Final Exam June a) y = x + 4 b) y = 2x + 5 c) y = 3x +2 d) y = 2x + 3
Part I- Multiple Choice: 2 points each: Select the best possible answer. 1) The nutrition label of cookies states that there are 20 servings in a box and that one serving contains 1.5 grams of fat. Kyle
More informationGraph the linear inequality. 1) x + 2y 6
Assignment 7.1-7.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the linear inequality. 1) x + 2y 6 1) 1 2) x + y < -3 2) 2 Graph the
More informationMathematical Games and Random Walks
Mathematical Games and Random Walks Alexander Engau, Ph.D. Department of Mathematical and Statistical Sciences College of Liberal Arts and Sciences / Intl. College at Beijing University of Colorado Denver
More informationISE 330 Introduction to Operations Research: Deterministic Models. What is Linear Programming? www-scf.usc.edu/~ise330/2007. August 29, 2007 Lecture 2
ISE 330 Introduction to Operations Research: Deterministic Models www-scf.usc.edu/~ise330/007 August 9, 007 Lecture What is Linear Programming? Linear Programming provides methods for allocating limited
More informationSystems of Equations. Red Company. Blue Company. cost. 30 minutes. Copyright 2003 Hanlonmath 1
Chapter 6 Systems of Equations Sec. 1 Systems of Equations How many times have you watched a commercial on television touting a product or services as not only the best, but the cheapest? Let s say you
More informationAlgebraic expression is formed from variables and constants using different operations. NCERT
UNIT 10 ALGEBRAIC EXPRESSIONS (A) Main Concepts and Results Algebraic expression is formed from variables and constants using different operations. Expressions are made up of terms. A term is the product
More informationQueuing Analysis. Chapter Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall
Queuing Analysis Chapter 13 13-1 Chapter Topics Elements of Waiting Line Analysis The Single-Server Waiting Line System Undefined and Constant Service Times Finite Queue Length Finite Calling Problem The
More informationM.Sc. (Final) DEGREE EXAMINATION, MAY Final Year. Statistics. Paper I STATISTICAL QUALITY CONTROL. Answer any FIVE questions.
(DMSTT ) M.Sc. (Final) DEGREE EXAMINATION, MAY 0. Final Year Statistics Paper I STATISTICAL QUALITY CONTROL Time : Three hours Maximum : 00 marks Answer any FIVE questions. All questions carry equal marks..
More informationLinear Programming. Businesses seek to maximize their profits while operating under budget, supply, Chapter
Chapter 4 Linear Programming Businesses seek to maximize their profits while operating under budget, supply, labor, and space constraints. Determining which combination of variables will result in the
More informationUNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION
MATHEMATICAL ECONOMICS COMPLEMENTARY COURSE B.Sc. Mathematics II SEMESTER UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Calicut University P. O. Malappuram, Kerala, India 67 65 40 UNIVERSITY OF CALICUT
More informationTRANSPORTATION PROBLEMS
63 TRANSPORTATION PROBLEMS 63.1 INTRODUCTION A scooter production company produces scooters at the units situated at various places (called origins) and supplies them to the places where the depot (called
More information56:171 Operations Research Final Exam December 12, 1994
56:171 Operations Research Final Exam December 12, 1994 Write your name on the first page, and initial the other pages. The response "NOTA " = "None of the above" Answer both parts A & B, and five sections
More informationBOARD QUESTION PAPER : MARCH 2018
Board Question Paper : March 08 BOARD QUESTION PAPER : MARCH 08 Notes: i. All questions are compulsory. Figures to the right indicate full marks. i Graph paper is necessary for L.P.P iv. Use of logarithmic
More informationLecture Notes. Applied Mathematics for Business, Economics, and the Social Sciences (4th Edition); by Frank S. Budnick
1 Lecture Notes Applied Mathematics for Business, Economics, and the Social Sciences (4th Edition); by Frank S. Budnick 2 Chapter 2: Linear Equations Definition: Linear equations are first degree equations.
More informationMATH 2070 Test 3 (Sections , , & )
Multiple Choice: Use a #2 pencil and completely fill in each bubble on your scantron to indicate the answer to each question. Each question has one correct answer. If you indicate more than one answer,
More informationOptimization Methods in Management Science
Problem Set Rules: Optimization Methods in Management Science MIT 15.053, Spring 2013 Problem Set 1 (First Group of Students) Students with first letter of surnames A F Due: February 12, 2013 1. Each student
More informationMath Week in Review #7
Math 166 Fall 2008 c Heather Ramsey Page 1 Math 166 - Week in Review #7 Section 4.3 - Gauss Elimination for Systems of Linear Equations When a system of linear equations has only two variables, each equation
More informationPaper Reference R. Statistics S4 Advanced/Advanced Subsidiary. Friday 21 June 2013 Morning Time: 1 hour 30 minutes
Centre No. Candidate No. Paper Reference(s) 6686/01R Edexcel GCE Statistics S4 Advanced/Advanced Subsidiary Friday 21 June 2013 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical
More informationUNIVERSITY of LIMERICK
UNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH Department of Mathematics & Statistics Faculty of Science and Engineering END OF SEMESTER ASSESSMENT PAPER MODULE CODE: MS4303 SEMESTER: Spring 2018 MODULE TITLE:
More informationTennessee Comprehensive Assessment Program TCAP. TNReady Algebra II Part I PRACTICE TEST. Student Name. Teacher Name
Tennessee Comprehensive Assessment Program TCAP TNReady Algebra II Part I PRACTICE TEST Student Name Teacher Name Tennessee Department of Education Algebra II, Part I Directions This booklet contains constructed-response
More informationReview Assignment II
MATH 11012 Intuitive Calculus KSU Name:. Review Assignment II 1. Let C(x) be the cost, in dollars, of manufacturing x widgets. Fill in the table with a mathematical expression and appropriate units corresponding
More informationSensitivity Analysis and Duality in LP
Sensitivity Analysis and Duality in LP Xiaoxi Li EMS & IAS, Wuhan University Oct. 13th, 2016 (week vi) Operations Research (Li, X.) Sensitivity Analysis and Duality in LP Oct. 13th, 2016 (week vi) 1 /
More informationQ3) a) Explain the construction of np chart. b) Write a note on natural tolerance limits and specification limits.
(DMSTT 21) Total No. of Questions : 10] [Total No. of Pages : 02 M.Sc. DEGREE EXAMINATION, MAY 2017 Second Year STATISTICS Statistical Quality Control Time : 3 Hours Maximum Marks: 70 Answer any Five questions.
More informationDecision Mathematics D2 Advanced/Advanced Subsidiary. Thursday 6 June 2013 Morning Time: 1 hour 30 minutes
Paper Reference(s) 6690/01R Edexcel GE Decision Mathematics D2 Advanced/Advanced Subsidiary Thursday 6 June 2013 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included with
More informationSocial Studies 3 Vocabulary Cards. century. History 1. period of 100 years
century History 1 period of 100 years chronological History 1 in order of time decade History 1 period of 10 years timeline History 1 list of important events in the order in which they happened year History
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) A) Not defined B) - 2 5
Stud Guide for TEST I Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the slope of the line passing through the given pair of points. )
More informationTutorial letter 201/2/2018
DSC1520/201/2/2018 Tutorial letter 201/2/2018 Quantitative Modelling 1 DSC1520 Semester 2 Department of Decision Sciences Solutions to Assignment 1 Bar code Dear Student This tutorial letter contains the
More informationMATH 445/545 Homework 1: Due February 11th, 2016
MATH 445/545 Homework 1: Due February 11th, 2016 Answer the following questions Please type your solutions and include the questions and all graphics if needed with the solution 1 A business executive
More informationMVE165/MMG630, Applied Optimization Lecture 6 Integer linear programming: models and applications; complexity. Ann-Brith Strömberg
MVE165/MMG630, Integer linear programming: models and applications; complexity Ann-Brith Strömberg 2011 04 01 Modelling with integer variables (Ch. 13.1) Variables Linear programming (LP) uses continuous
More informationLesson 6.1 Recursive Routines
Lesson 6.1 Recursive Routines 1. Give the starting value and constant multiplier for each sequence. Then find the fifth term. a. 4800, 1200, 300,... b. 21, 44.1, 92.61,... c. 100, 90, 81,... d. 100, 101,
More informationMATH 2070 Test 3 (Sections , , & )
Multiple Choice: Use a #2 pencil and completely fill in each bubble on your scantron to indicate the answer to each question. Each question has one correct answer. If you indicate more than one answer,
More information56:171 Fall 2002 Operations Research Quizzes with Solutions
56:7 Fall Operations Research Quizzes with Solutions Instructor: D. L. Bricker University of Iowa Dept. of Mechanical & Industrial Engineering Note: In most cases, each quiz is available in several versions!
More informationInteger Programming (IP)
Integer Programming (IP) An LP problem with an additional constraint that variables will only get an integral value, maybe from some range. BIP binary integer programming: variables should be assigned
More informationMethods and Models for Combinatorial Optimization
Methods and Models for Combinatorial Optimization Modeling by Linear Programming Luigi De Giovanni, Marco Di Summa Dipartimento di Matematica, Università di Padova De Giovanni, Di Summa MeMoCO 1 / 35 Mathematical
More informationARITHMETIC PROGRESSIONS
ARITHMETIC PROGRESSIONS 93 ARITHMETIC PROGRESSIONS 5 5.1 Introduction You must have observed that in nature, many things follow a certain pattern, such as the petals of a sunflower, the holes of a honeycomb,
More information