ORI 390Q Models and Analysis of Manufacturing Systems First Exam, fall 1994
|
|
- Candace Woods
- 5 years ago
- Views:
Transcription
1 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 M1 M2 O A (10,0.1) 7 8 V B (8,0.2) M4 2 4 M5 The figure shows the processes for two products. The operation times and defect rates are shown on the figure. s are in minutes. Inspections are perfect. Machine assignments are shown adjacent to the operations. Note that machines M1 and M2 are used for both products. Product A is made from a single raw material 1. Product B is made from two raw materials, 1 and 2. The table below gives the maximum sales and revenues for the products, and the unit costs for the raw materials. Assume 0 hours per week and 60 minutes per hour. The information on this page is used for several problems in the exam. You may use the results of one problem to aid in the analyses of the others. Finished Goods Max. Sales per week Revenue per unit of finished good Raw materials A 100/week $58 1 $0 B 100/week $95 2 $20 Cost per unit of raw material 1
2 Process A Name Index Next Oper. Defect Rate Defects Out Remove d A Start Op5 Op % M % 0.0% In6 In % Insp % 5.0% A End % % 0.0% 1 0 Ratio Unit Process B Name Index Next B Start Oper. Defect Rate Defects Out Remove d Op4 Op % M % 0.0% Op7 Op % M % 0.0% Op8 In % Insp % 28.0% B End % % 0.0% 1 0 Ratio Unit Process C Name Index Next Oper. Defect Rate Defects Out Remove d C Start Op1 Op % M % 0.0% Op2 Op % M % 0.0% In In % Insp % 1.5% C End % % 0.0% 1 0 Ratio Unit 2
3 1. (20 Points) The number of machines available for each type is shown in the table below. M1 M2 M M4 M5 Number Unlimited We identify three modules in the problem: Module A: operations 5 and 6, Module B: operations 4, 7, and 8, Module C: operations 1, 2 and. Write the linear programming model that will determine the optimum product mix. Include variables for the three modules and the raw material amounts. Total Name: A B C 1 2 Values: Linear Obj. Coef.: Lower Bounds: Upper Bounds: E+07 1E+07 Constraints Name Constraint Coefficients M M M M M = = 0 Con = 0 Max 58A + 95B + 9C subject to: M1: 18.5C 5400 M2: 17.C 600 M: 12.62A 1800 M4: 1.889B 1800 M5: A : C -1 = 0 2: 1.889B -2 = 0 Conservation: A B - C = 0 0 A 100, 0 B 100, C 0, 1 0, 2 0
4 (10 Points) For the situation in the figure, what is the throughput dollars per unit for each product? The throughput dollars per unit is the revenue raw material cost. For A: 58 u 1 *u 5 *0 (we must multiply the two flow ratios together to find the amount of 1 per unit of A. TP$ A = 58* - (1.24)*(1.056)*0 = 50 0*1.299 = For B: 95 u 1 *u 7 *0 u 4 *20 TP$ B = : 95 (1. 24)(1.89) * *20 = (10 Points) After the linear programming model is solved, we discover the following information from the sensitivity analysis. The reduced cost for product B is 9.22, and all the other reduced costs are zero. The dual variable for the constraint for machine M2 is 1.1. What do these two numbers tell you? The value of 9.22 indicates the value of increasing the market for product B by 1 unit. The value of 1.1 is the increase in the objective by increasing the availability of machine 2 by 1-minute. 4
5 . (20 Points) It turns out that the market demand for product B is a bottleneck and the time available on machine M2 is a bottleneck. We would like to get more profit from the business. Evaluate the following changes as to whether or not the throughput will increase after the change. Explain your reasoning briefly. Action Invest in a marketing strategy that will increase the maximum sales of product A. Improve the Throughput? Why or Why not? This will not help. Product B is not a bottleneck. You might have a greater demand, but you won t sell any more. The throughput will stay the same. Outsource some of the production of module C. The cost per unit of the product from the outside supplier is $40. This material has no defects. This might help because it will take some load off the M2 machine and allow more production of product B. The raw material cost for module C per unit out of C is 0*u 1 = 0*1.246.= 7.0. Although the outsourceing cost is greater, the TP will be increased. Add an inspection station after operation 4. This change will reduce the flow ratio for operation 7 and thus the amount of time per unit of B on the bottleneck machine. Thus change will allow more production of B. It also will reduce the cost of 1 for product B. Add an inspection operation after operation 1. This change will have the effect of reducing the flow ratio for operation 2. Thus more product will be able to be manufactured on machine 2. The throughput will increase. 5
6 4. (20 Points) You decide to manufacture the products on two separate lines. The processes now appear as in the figure below. (time, defect rate) (16,0.07) (15,0.07) (5,0) (12,0.05) V A M1 M2 M (16,0.07) (15,0.07) (5,0) (10,0.1) A 7 8 V B M1 M2 (8,0.2) M4 2 4 M5 The allocation of machines to the two lines is indicated in the table below. Machines now produce only one product. How does this change the product mix? Is separating the lines a good idea? Machine Assignment for Process A M1 M2 M M4 M5 Number Unlimited Machine Assignment for Process B M1 M2 M M4 M5 Number Unlimited With this information each product has its own bottleneck. Based on the unit times, the bottleneck for product A is machine 1. The maximum production is 1800/2.7 = 92 units The bottleneck for product B is M2 with the maximum production allowed of 74 units. This is not a good idea, since the throughput of both products is reduced. 6
7 6. (10 Points) Now consider only the system for product B. We decide to manufacture 150 units per week of product B. We will provide as many machines of each type as necessary. (16,0.07) (15,0.07) (5,0) (10,0.1) A 7 8 V B M1 M2 (8,0.2) M4 2 4 M5 In addition to the information in the figure, we discover an unexplained delay of 0 minutes in front of each inspection operation. a. What is the value of WIP for this production rate? We must compute the WIP for three separate parts since the flow the parts is different and the Raw material contents is different. For operations 1, 2 and, the flow is *150 = 241. The residence time is = 66 min or weeks The WIP is 241* = 8.82 units The value of the WIP is 8.82*0 = For operation 4, the flow is 1.889*150 = 208. The residence time is 8 min or weeks The WIP is 208* = units The value of the WIP is *20 = $18.51 For operations 7 and 8, the flow is 1.889*150 = 208. The residence time is = 47 min or weeks The WIP is 208* = 5.44 units The value of the WIP is 5.44 *50 = $ Total WIP is Total Value of WIP is $555 b. What is the throughput time for a unit of product? The throughput time is the time for the longest path (1. 2., 7, 8). Add 1 hour for the inspection delays. The time is = 11 minutes. c. How much raw material of 1 must be supplied for this production rate? The amount of 1 is 150 u 1 = 150* =
8 7. (6 Points) In the book The Goal, the heat-treat process is discovered as a bottleneck. Give three specific examples of steps taken to exploit the heat-treat process. I'm particularly interested in exploiting rather than elevating or subordinating. Exploiting the heat-treat is getting as much out of the current capacity as possible. Some steps taken in the book are: Station a worker at the heat-treat machine so that it is never idle after it finishes the job. Try to make larger batches by adding parts with similar processing times. Improve the setup process so that the heat-treat machine is not delayed because of setup. 8 (4 Points) Give one example of steps taken to elevate, rather than exploit the heattreat process. An example of elevating was to outsource the heat-treat process. Another is to re-engineer the products so as not to require heat-treat. 8
Deterministic 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 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 informationExam of Discrete Event Systems
Exam of Discrete Event Systems - 04.02.2016 Exercise 1 A molecule can switch among three equilibrium states, denoted by A, B and C. Feasible state transitions are from A to B, from C to A, and from B to
More informationST. 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 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 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 informationSchool of Business. Blank Page
Maxima and Minima 9 This unit is designed to introduce the learners to the basic concepts associated with Optimization. The readers will learn about different types of functions that are closely related
More informationA Semiconductor Wafer
M O T I V A T I O N Semi Conductor Wafer Fabs A Semiconductor Wafer Clean Oxidation PhotoLithography Photoresist Strip Ion Implantation or metal deosition Fabrication of a single oxide layer Etching MS&E324,
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 informationCOMP9334: Capacity Planning of Computer Systems and Networks
COMP9334: Capacity Planning of Computer Systems and Networks Week 2: Operational analysis Lecturer: Prof. Sanjay Jha NETWORKS RESEARCH GROUP, CSE, UNSW Operational analysis Operational: Collect performance
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 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 informationLP Definition and Introduction to Graphical Solution Active Learning Module 2
LP Definition and Introduction to Graphical Solution Active Learning Module 2 J. René Villalobos and Gary L. Hogg Arizona State University Paul M. Griffin Georgia Institute of Technology Background Material
More informationSystems Optimization and Analysis Optimization Project. Labor Planning for a Manufacturing Line
15.066 Systems Optimization and Analysis Optimization Project Labor Planning for a Manufacturing Line Team 1 The Tek Team Lane Ballard Christine Cheung Justin Ging Omur Kaya David Jackson Alyson Naughton
More informationPractice A Exam 3. November 14, 2018
Department of Mathematics University of Notre Dame Math 10250 Elem. of Calc. I Name: Instructor: Practice A Exam November 14, 2018 This exam is in 2 parts on 11 pages and contains 15 problems worth a total
More informationIntroduction to Operations Research Economics 172A Winter 2007 Some ground rules for home works and exams:
Introduction to Operations Research Economics 172A Winter 2007 Some ground rules for home works and exams: Write your homework answers on the sheets supplied. If necessary, you can get new sheets on the
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 informationLinear Programming CHAPTER 11 BASIC CONCEPTS AND FORMULA. Basic Concepts 1. Linear Programming
CHAPTER 11 Linear Programming Basic Concepts 1. Linear Programming BASIC CONCEPTS AND FORMULA Linear programming is a mathematical technique for determining the optimal allocation of re- sources nd achieving
More informationLINEAR PROGRAMMING BASIC CONCEPTS AND FORMULA
CHAPTER 11 LINEAR PROGRAMMING Basic Concepts 1. Linear Programming BASIC CONCEPTS AND FORMULA Linear programming is a mathematical technique for determining the optimal allocation of re- sources nd achieving
More informationFURTHER MATHEMATICS Units 3 & 4 - Written Examination 2
THIS BOX IS FOR ILLUSTRATIVE PURPOSES ONLY 2016 Examination Package - Trial Examination 4 of 5 Figures STUDENT NUMBER Letter Words FURTHER MATHEMATICS Units 3 & 4 - Written Examination 2 (TSSM s 2014 trial
More informationOptimisation. 3/10/2010 Tibor Illés Optimisation
Optimisation Lectures 3 & 4: Linear Programming Problem Formulation Different forms of problems, elements of the simplex algorithm and sensitivity analysis Lecturer: Tibor Illés tibor.illes@strath.ac.uk
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 informationMath 1325 Final Exam Review
Math 1325 Final Exam Review 1. The following table of values gives a company s annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to x = 0. Year 2003 2004 2005 2006
More informationIntroduction to Operations Research. Linear Programming
Introduction to Operations Research Linear Programming Solving Optimization Problems Linear Problems Non-Linear Problems Combinatorial Problems Linear Problems Special form of mathematical programming
More informationProgrammers A B C D Solution:
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
More informationA Markov chain analysis of the effectiveness of drum-buffer-rope material flow management in job shop environment
International Journal of Industrial Engineering Computations 6 (015) 457 468 Contents lists available at GrowingScience International Journal of Industrial Engineering Computations homepage: www.growingscience.com/iiec
More informationLINEAR PROGRAMMING: A GEOMETRIC APPROACH. Copyright Cengage Learning. All rights reserved.
3 LINEAR PROGRAMMING: A GEOMETRIC APPROACH Copyright Cengage Learning. All rights reserved. 3.4 Sensitivity Analysis Copyright Cengage Learning. All rights reserved. Sensitivity Analysis In this section,
More informationIntroduction to Operations Research
Introduction to Operations Research Linear Programming Solving Optimization Problems Linear Problems Non-Linear Problems Combinatorial Problems Linear Problems Special form of mathematical programming
More informationCLASS NOTES: BUSINESS CALCULUS
CLASS NOTES: BUSINESS CALCULUS These notes can be thought of as the logical skeleton of my lectures, although they will generally contain a fuller exposition of concepts but fewer examples than my lectures.
More informationProgram Name: PGDBA Production and Operations Management Assessment Name: POM - Exam Weightage: 70 Total Marks: 70
Program Name: PGDBA Subject: Production and Operations Management Assessment Name: POM - Exam Weightage: 70 Total Marks: 70 Duration: 60 mins Instructions (Start of Assessment): Marks: 70 Time: 60 Minutes
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 information1 Reminders. In-class exam in two weeks (Sept 28/29) Assignments are posted after every class. Lecture is for big picture
1 Reminders In-class exam in two weeks (Sept 28/29) pen and paper; no calculator; no notes practice problems are already posted online MLP test on same topics: take before 10/4 Assignments are posted after
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 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 informationManufacturing System Flow Analysis
Manufacturing System Flow Analysis Ronald G. Askin Systems & Industrial Engineering The University of Arizona Tucson, AZ 85721 ron@sie.arizona.edu October 12, 2005 How Many IEs Does It Take to Change a
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 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 informationCHAPTER 16: SCHEDULING
CHAPTER 16: SCHEDULING Solutions: 1. Job A B C A B C 1 5 8 6 row 1 0 3 1 Worker 2 6 7 9 reduction 2 0 1 3 3 4 5 3 3 1 2 0 column reduction A B C 1 0 2 1 Optimum: 2 0 0 3 Worker 1, Job A 3 1 1 0 2 B 3 C
More informationLinear Systems and Matrices. Copyright Cengage Learning. All rights reserved.
7 Linear Systems and Matrices Copyright Cengage Learning. All rights reserved. 7.1 Solving Systems of Equations Copyright Cengage Learning. All rights reserved. What You Should Learn Use the methods of
More informationIndustrial Processes I Manufacturing Economics
Industrial Processes I Manufacturing Economics Equipment Cost Rate (Example 1) A production machine is purchased for an initial cost plus installation of $500,000. Its anticipated life = 7 yrs. The machine
More information7.1Solvingsys2015.notebook. November 05, Warm up. Partial fraction decompostion
Warm up Partial fraction decompostion 1 Please add due dates to the calendar Nov Dec 2 7.1 Solving Systems of Equations by Substitution and Graphing Vocabulary System: Problems that involve two or more
More informationFinal exam.
EE364a Convex Optimization I March 14 15 or March 15 16, 2008. Prof. S. Boyd Final exam You may use any books, notes, or computer programs (e.g., Matlab, cvx), but you may not discuss the exam with anyone
More informationBike Plast DD some remarks
Roberto Cigolini roberto.cigolini@polimi.it Department of Management, Economics and Industrial Engineering Politecnico di Milano 1 Evaluate the analysis carried out by the Plant Director and comment on
More informationOnline Appendix for Coordination of Outsourced Operations at a Third-Party Facility Subject to Booking, Overtime, and Tardiness Costs
Submitted to Operations Research manuscript OPRE-2009-04-180 Online Appendix for Coordination of Outsourced Operations at a Third-Party Facility Subject to Booking, Overtime, and Tardiness Costs Xiaoqiang
More informationMath 1314 Final Exam Review. Year Profits (in millions of dollars)
Math 1314 Final Exam Review 1. The following table of values gives a company s annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to x = 0. Year 2003 2004 2005 2006
More informationLecture 6: Sections 2.2 and 2.3 Polynomial Functions, Quadratic Models
L6-1 Lecture 6: Sections 2.2 and 2.3 Polynomial Functions, Quadratic Models Polynomial Functions Def. A polynomial function of degree n is a function of the form f(x) = a n x n + a n 1 x n 1 +... + a 1
More informationApril 2003 Mathematics 340 Name Page 2 of 12 pages
April 2003 Mathematics 340 Name Page 2 of 12 pages Marks [8] 1. Consider the following tableau for a standard primal linear programming problem. z x 1 x 2 x 3 s 1 s 2 rhs 1 0 p 0 5 3 14 = z 0 1 q 0 1 0
More informationANALYSIS OF AUTOMATED FLOW LINE & LINE BALANCING
UNIT 3: ANALYSIS OF AUTOMATED FLOW LINE & LINE BALANCING General Terminology & Analysis: There are two problem areas in analysis of automated flow lines which must be addressed: 1. Process Technology 2.
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 132 Eam 2 Review (.1 -.5, 7.1-7.5) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the given ordered set of numbers is a solution
More information1.4 Linear Functions of Several Variables
.4 Linear Functions of Several Variables Question : What is a linear function of several independent variables? Question : What do the coefficients of the variables tell us? Question : How do you find
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 informationMACHINE DEDICATION UNDER PRODUCT AND PROCESS DIVERSITY. Darius Rohan. IBM Microelectonics Division East Fishkill, NY 12533, U.S.A.
Proceedings of the 1999 Winter Simulation Conference P. A. Farrington, H. B. Nembhard, D. T. Sturrock, and G. W. Evans, eds. MACHINE DEDICATION UNDER PRODUCT AND PROCESS DIVERSITY Darius Rohan IBM Microelectonics
More informationMath 116: Business Calculus Chapter 4 - Calculating Derivatives
Math 116: Business Calculus Chapter 4 - Calculating Derivatives Instructor: Colin Clark Spring 2017 Exam 2 - Thursday March 9. 4.1 Techniques for Finding Derivatives. 4.2 Derivatives of Products and Quotients.
More informationEcon 172A, Fall 2012: Final Examination (I) 1. The examination has seven questions. Answer them all.
Econ 172A, Fall 12: Final Examination (I) Instructions. 1. The examination has seven questions. Answer them all. 2. If you do not know how to interpret a question, then ask me. 3. Questions 1- require
More informationNON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer x y
NON-CALCULATOR: I. Decide whether or not the following information defines a function. Explain/support your answer. 1. 2. 3. x -1 0 1 2 3 y 5 7 2-1 -8 4 & 5. Refer to the numbered graphs 4 5 6. x -3 2
More informationCalculus in Business. By Frederic A. Palmliden December 7, 1999
Calculus in Business By Frederic A. Palmliden December 7, 999 Optimization Linear Programming Game Theory Optimization The quest for the best Definition of goal equilibrium: The equilibrium state is defined
More information12-1. Example 1: Which relations below represent functions? State the domains and ranges. a) {(9,81), (4,16), (5,25), ( 2,4), ( 6,36)} Function?
MA 000, Lessons a and b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1. and.1 Definition: A relation is any set of ordered pairs. The set of first components in the ordered
More informationExam 3 Review Math 118 Sections 1 and 2
Exam 3 Review Math 118 Sections 1 and 2 This exam will cover sections 5.3-5.6, 6.1-6.3 and 7.1-7.3 of the textbook. No books, notes, calculators or other aids are allowed on this exam. There is no time
More informationHow to handle and solve a linear equation (what s a linear equation?) How to draw the solution set for a linear inequality
Study guide for final exam, Math 1090 - College Algebra for Business and Social Sciences This guide is meant to be a help on studying what I think is most important important that you learn form this exam,
More information1.4 CONCEPT QUESTIONS, page 49
.4 CONCEPT QUESTIONS, page 49. The intersection must lie in the first quadrant because only the parts of the demand and supply curves in the first quadrant are of interest.. a. The breakeven point P0(
More informationMAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.
MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the
More informationUnderstanding the Simplex algorithm. Standard Optimization Problems.
Understanding the Simplex algorithm. Ma 162 Spring 2011 Ma 162 Spring 2011 February 28, 2011 Standard Optimization Problems. A standard maximization problem can be conveniently described in matrix form
More informationIntroduction to Operations Research Prof G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras
Introduction to Operations Research Prof G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Module 01 Linear Programming Introduction and formulations Lecture - 01 Product
More informationSystems of Linear Equations in Two Variables. Break Even. Example. 240x x This is when total cost equals total revenue.
Systems of Linear Equations in Two Variables 1 Break Even This is when total cost equals total revenue C(x) = R(x) A company breaks even when the profit is zero P(x) = R(x) C(x) = 0 2 R x 565x C x 6000
More informationMAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29,
MAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29, This review includes typical exam problems. It is not designed to be comprehensive, but to be representative of topics covered
More informationMODELING (Integer Programming Examples)
MODELING (Integer Programming Eamples) IE 400 Principles of Engineering Management Integer Programming: Set 5 Integer Programming: So far, we have considered problems under the following assumptions:
More informationExtrema and the First-Derivative Test
Extrema and the First-Derivative Test MATH 151 Calculus for Management J. Robert Buchanan Department of Mathematics 2018 Why Maximize or Minimize? In almost all quantitative fields there are objective
More informationMATH150-E01 Test #2 Summer 2016 Show all work. Name 1. Find an equation in slope-intercept form for the line through (4, 2) and (1, 3).
1. Find an equation in slope-intercept form for the line through (4, 2) and (1, 3). 2. Let the supply and demand functions for sugar be given by p = S(q) = 1.4q 0.6 and p = D(q) = 2q + 3.2 where p is the
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 informationSolution Cases: 1. Unique Optimal Solution Reddy Mikks Example Diet Problem
Solution Cases: 1. Unique Optimal Solution 2. Alternative Optimal Solutions 3. Infeasible solution Case 4. Unbounded Solution Case 5. Degenerate Optimal Solution Case 1. Unique Optimal Solution Reddy Mikks
More informationMulticriteria Decision Making
Multicriteria Decision Making Goal Programming Multicriteria Decision Problems Goal Programming Goal Programming: Formulation and Graphical Solution 1 Goal Programming Goal programming may be used to solve
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 informationUnit 4: Inequalities. Inequality Symbols. Algebraic Inequality. Compound Inequality. Interval Notation
Section 4.1: Linear Inequalities Section 4.2: Solving Linear Inequalities Section 4.3: Solving Inequalities Applications Section 4.4: Compound Inequalities Section 4.5: Absolute Value Equations and Inequalities
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 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 informationUnits and Dimensional Analysis
LESSON Units and Dimensional Analysis UNDERSTAND When solving a problem, it is important to correctly identify the units being considered or measured. This may require converting a quantity given in one
More informationCONTINUOUS FLOW CHEMISTRY (PROCESSING) FOR INTERMEDIATES AND APIs
CONTINUOUS FLOW CHEMISTRY (PROCESSING) FOR INTERMEDIATES AND APIs Sripathy Venkatraman, Section Head at AMRI Abstract Many contract manufacturing organizations (CMOs) offer continuous flow chemistry, but
More informationMath Want to have fun with chapter 4? Find the derivative. 1) y = 5x2e3x. 2) y = 2xex - 2ex. 3) y = (x2-2x + 3) ex. 9ex 4) y = 2ex + 1
Math 160 - Want to have fun with chapter 4? Name Find the derivative. 1) y = 52e3 2) y = 2e - 2e 3) y = (2-2 + 3) e 9e 4) y = 2e + 1 5) y = e - + 1 e e 6) y = 32 + 7 7) y = e3-1 5 Use calculus to find
More informationCORE. Chapter 3: Interacting Linear Functions, Linear Systems. Algebra Assessments
CORE Algebra Assessments Chapter 3: Interacting Linear Functions, Linear Systems 97 98 Bears Band Booster Club The Bears Band Booster Club has decided to sell calendars to the band members and their parents.
More informationChapter 2: Introduction to Linear Programming
Chapter 2: Introduction to Linear Programming You may recall unconstrained optimization from your high school years: the idea is to find the highest point (or perhaps the lowest point) on an objective
More informationChapter 2 Introduction to Optimization and Linear Programming
Ch. 2 Introduction to Optimization and Linear Programming TB-9 Chapter 2 Introduction to Optimization and Linear Programming Multiple Choice 1. What most motivates a business to be concerned with efficient
More informationStudy Guide - Part 2
Math 116 Spring 2015 Study Guide - Part 2 1. Which of the following describes the derivative function f (x) of a quadratic function f(x)? (A) Cubic (B) Quadratic (C) Linear (D) Constant 2. Find the derivative
More informationExercises - Linear Programming
Chapter 38 Exercises - Linear Programming By Sariel Har-Peled, December 10, 2007 1 Version: 1.0 This chapter include problems that are related to linear programming. 38.1 Miscellaneous Exercise 38.1.1
More informationOnline Math 1314 Final Exam Review
Online Math 1314 Final Exam Review 1. The following table of values gives a company s annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to x = 0. Year 2003 2004
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Linear equations 1 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Find the slope of the line passing through the points (, -3) and (2, -1). 1)
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 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 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 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 informationMA 181 Lecture Chapter 7 College Algebra and Calculus by Larson/Hodgkins Limits and Derivatives
7.5) Rates of Change: Velocity and Marginals MA 181 Lecture Chapter 7 College Algebra and Calculus by Larson/Hodgkins Limits and Derivatives Previously we learned two primary applications of derivatives.
More informationThe Graphical Method & Algebraic Technique for Solving LP s. Métodos Cuantitativos M. En C. Eduardo Bustos Farías 1
The Graphical Method & Algebraic Technique for Solving LP s Métodos Cuantitativos M. En C. Eduardo Bustos Farías The Graphical Method for Solving LP s If LP models have only two variables, they can be
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 informationEC611--Managerial Economics
EC611--Managerial Economics Optimization Techniques and New Management Tools Dr. Savvas C Savvides, European University Cyprus Models and Data Model a framework based on simplifying assumptions it helps
More informationFinal Exam Aug. 29th Mathematical Foundations in Finance (FIN 500J) Summer, Sample Final Exam
Final Exam Aug. 29th 2009 1 Olin Business School Yajun Wang Mathematical Foundations in Finance (FIN 500J) Summer, 2009 Sample Final Exam NAME (Print Clearly): Instructions 1. You have 90 minutes to complete
More informationPage Points Score Total: 100
Math 1130 Spring 2019 Sample Exam 1c 1/31/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 8 pages (including this cover page) and 7 problems. Check to see if any pages
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 informationVCE Further Mathematics Units 3&4
Trial Examination 2016 VCE Further Mathematics Units 3&4 Written Examination 2 Question and Answer Booklet Reading time: 15 minutes Writing time: 1 hour 30 minutes Student s Name: Teacher s Name: Structure
More informationMaximums and Minimums
Maximums and Minimums Lecture 25 Section 3.1 Robb T. Koether Hampden-Sydney College Mon, Mar 6, 2017 Robb T. Koether (Hampden-Sydney College) Maximums and Minimums Mon, Mar 6, 2017 1 / 9 Objectives Objectives
More informationEcon 8208 Homework 2 Due Date: May 7
Econ 8208 Homework 2 Due Date: May 7 1 Preliminaries This homework is all about Hierarchical Linear Bayesian Models (HLBM in what follows) The formal setup of these can be introduced as follows Suppose
More informationApplications of Systems of Linear Inequalities
Applications of Systems of Linear Inequalities Finite Math 26 April 2017 Finite Math Applications of Systems of Linear Inequalities 26 April 2017 1 / 17 Quiz What does it mean for a feasible region to
More information