The Simplex Method: Learning Team A Mike Smith, Todd Jones Math212/Introduction to Finite Mathematics February 1, 2011 The Simplex... Method: Learning Team A Sam’s Hairbows and Accessories is a small company preparing for the next scheduled craft fair. The owners, Sam and Todd, both have full-time jobs in addition to owning the company so they are only able to spend a combined total of 80 hours labor to prepare for the fair in four weeks. Sam’s offers five main product lines: basic bows, elaborate...
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Phase Simplex Method Consider the following LP problem. max z = 2x1 + 3x2 + x3... s.t. x1 + x2 + x3 · 40 2x1 + x2 ¡ x3 ¸ 10 ¡x2 + x3 ¸ 10 x1; x2; x3 ¸ 0 It can be transformed into the standard form by introducing 3 slack variables x4, x5 and x6. max z = 2x1 + 3x2 + x3 s.t. x1 + x2 + x3 + x4 = 40 2x1 + x2 ¡ x3 ¡ x5 = 10 ¡x2 + x3 ¡ x6 = 10 x1; x2; x3; x4; x5; x6 ¸ 0 There is no obvious initial basic feasible solution, and it is not even known whether there exists one. We can use Phase I method...
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Recognize special cases such as infeasibility, unboundedness and degeneracy. 5. Use the simplex tables to conduct sensitivity analysis. 6.... Construct the dual problem from the primal problem. Linear Programming: The Simplex Method LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex...
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questions 1. a. Explain how and why Operation Research methods have been valuable in aiding executive decisions. [5 Marks] b. Discuss the... usefulness of Operation Research in decision making process and the role of computers in this field. [5 Marks] 2. Explain how the linear programming technique can be helpful in decision-making in the areas of Marketing and Finance. [10 Marks] 3. a. How do you recognise optimality in the simplex method? b. Write the role of pivot element in simplex table? ...
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research which is very easy to use. Further, TORA is menu-driven and Windows-based which makes it very user friendly. The software can be... executed in automated or tutorial mode. The automated mode reports the final solution of the problem, usually in the standard format followed in commercial packages, while the tutorial mode keeps on giving step-wise information about the methodology and solution. TORA tutorial software deals with the following algorithms: •Solution...
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Simplex Method Paper Simplex Method Paper Many people may be wondering exactly what the simplex method is.... The simplex method definition is a method for solving linear programming problems. According to Barnett, Byleen, and Karl (2011) the simplex method is used routinely on applied problems involving thousands of variables and problem constraints. George B. Dantzig developed the simplex method in 1947. In this paper the topic of discussion includes how to solve a simplex method problem that...
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Solutions to LP Practice Problems[1] 1. Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair... uses 3 units of wood. A desk contributes $40 to profit, and a chair contributes $25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 20 units of wood available. Using the graph below, determine a production plan that maximizes Furnco’s profit. a) Draw isoprofit lines where the total profit equals...
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Consider the following linear programming problem: Min z = 3x12x23x3 Subject to x1+2x2 +x3 14... x1+2x2+4x3 12 x1 x2 +x3 = 2 x3 3 x1; x2 unrestricted (a) [6 points] Reformulate the problem so it is in standard format. (b) [6 points] Reformulate the problem so it is in canonical format. (c) [3 points] Convert the problem into a maximization problem. 2. [20 points] A lathe is used to reduce the diameter of a steel shaft whose length is 36 inches (in.) from 14 in. to 12 in. The speed x1 (in revolutions...
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Lesson 9 : The Big M Method Learning outcomes • The Big M Method to solve a linear programming problem. In the... previous discussions of the Simplex algorithm I have seen that the method must start with a basic feasible solution. In my examples so far, I have looked at problems that, when put into standard LP form, conveniently have an all slack starting solution. An all slack solution is only a possibility when all of the constraints in the problem have or = constraints, a starting basic feasible...
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as 3 separate constraints in an integer program. Answer Selected Answer: False Correct Answer: False . Question 2 2 out of... 2 points Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Answer Selected Answer: False Correct Answer: False . Question 3 2 out of 2 points If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional...
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a.|objectives, resources, goals.| b.|decisions, constraints, an objective.| c.|decision variables, profit levels, costs.| d.|decisions,... resource requirements, a profit function.| ___A_ 2. What is the goal in optimization? a.|Find the best decision variable values that satisfy all constraints.| b.|Find the values of the decision variables that use all available resources.| c.|Find the values of the decision variables that satisfy all constraints.| d.|None of the above.| ____B 3. Limited resources...
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Graphical Solution Method Linear Programming Model Simplex method Solution Solving Linear Programming Problems with Excel Dr A... Lung Student exercises Kingston University London 1 Linear Programming (LP) • A model consisting of linear relationships representing a firm’s objective and resource constraints • LP is a mathematical modeling technique used to determine a level of operational activity in order to achieve an objective, subject to restrictions called constraints • Pioneered by George...
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Online Tutorial The Simplex Method of Linear Programming Tutorial Outline CONVERTING THE CONSTRAINTS TO EQUATIONS... SOLVING MINIMIZATION PROBLEMS SETTING UP THE FIRST SIMPLEX TABLEAU KEY TERMS SIMPLEX SOLUTION PROCEDURES SOLVED PROBLEM SUMMARY OF SIMPLEX STEPS FOR MAXIMIZATION PROBLEMS DISCUSSION QUESTIONS ARTIFICIAL AND SURPLUS VARIABLES SUMMARY PROBLEMS 3 T 3-2 O N L I N E T U T O R I A L 3 THE SIMPLEX METHOD OF L I N E A R P RO G R A M M I N...
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Quantitative Methods: MAT540 Quiz 5 • Question 1 If we are solving a 0-1 integer programming problem, the constraint... x1 ≤ x2 is a conditional constraint. Answer Selected Answer: True Correct Answer: True • Question 2 If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint. Answer Selected Answer: False Correct Answer: False • Question 3 If we...
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respectively. Formulate the problem as a linear programming problem. Solution: Let x and y denote the number of production runs of the two processes,... respectively. Then the appropriate mathematical formulation of the problem is: Maximize Z=200x+300y Subject to the constraints: 4x+5y≤225 3x+6y≤200 4x+5y≥150 7x+5y≥120 x,y≥0 The standard weight of a special purpose brick is equal to 5kg and it contains two basic ingredients B1 and B2. B1 costs Nu. 5 per kg and B2 costs...
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Assignment #3: Julia’s Food Booth Quantitative Methods 540 Buddy L. Bruner, Ph.D. Shirley Foster 11/25/2012... Assignment 3: Case problem “Julia’s Food Booth” Page 1 A. Julia Robertson is making an allowance for renting a food booth at her school. She is seeking ways to finance her last year and believed that a food booth outside her school’s stadium would be ideal. Her goal is to earn the most money possible thus increasing her earnings. In this case...
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OFFICE EXCEL2 3.1.1 EXCEL DATA INPUT AND SOLVE THE PROBLEM2 3.1.2 ANSWER ANALYSIS3 3.1.3 SENSITIVITY ANALYSIS4 3.2 XPRESS-IVE... ANALYSIS6 4. CONCLUSION6 APPENDIX Operational Research Methods Report 1. Introduction Linear programming (LP) model is a significant and popular used model of operational research technique. It helps to optimize the objective value with constraints. LP model have three essential assumptions when use this model to solve problem. Firstly, proportionality and...
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its third chapter. Key words: linear programming; simplex method. I. Fundamentals and scope Based on a prototype example, Linear... Programming is presented, as well as the simplex method of resolution. This method was first presented by G. B. Dantzig in 1947 [MacTutor, 2007]. The text is based on the book by Hillier and Lieberman [2005], and begins with segments of the third chapter of the book. II. Explanation of the simplex method 3 Introduction to Linear Programming (H&L 25) The development...
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Statistics and Quantitative Methods ASSIGNMENT: 2 PREPARED FOR: CHOWDHURY PREPARED BY: VALLEY STATE UNIVERSITY DATE: 13.... The Electrotech Corporation manufactures two industrial-sized electrical devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires 2 hours of wiring and 1 hour of testing and can be sold for a $250 profit. Each alternator requires 3 hours of wiring and 2 hours of testing and can...
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margin or least time, when resources have alternative uses. The term ‛linear’ means that all inequations or equations used and the function... to be maximized or minimized are linear. That is why linear programming deals with that class of problems for which all relations among the variables involved are linear. Formally, linear programming deals with the optimization (maximization or minimization) of a linear function of a number of variables subject to a ¹equations in variables involved. The general...
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6S-2 Solving LP Models Using Excel, 6S-17 SUPPLEMENT TO CHAPTER LEARNING OBJECTIVES Linear Programming Model, 6S-2 Formulating... Some Other Types of Constraints, 6S-3 Sensitivity Analysis, 6S-19 Objective Function Coefficient Changes, 6S-20 Changes in the Right-Hand Side (RHS) Value of a Constraint, 6S-21 After completing this supplement, you should be able to: 1 Describe the type of problem Graphical Solution Method, 6S-4 Outline of Graphical Solution Method, 6S-4 Plotting...
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Page 1 7 MODULE Linear Programming: The Simplex Method LEARNING OBJECTIVES After completing this chapter, students will be able... to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex tableau. 4. Recognize special cases such as infeasibility, unboundedness and degeneracy. 5. Use the simplex tables to conduct sensitivity analysis. 6...
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Course MBA – 2nd Semester Subject Operations Research Assignment MB0048 – Set 1 Q.1. (a) what is linear programming... problem? (b) A toy company manufactures two types of dolls, a basic version doll- A and a deluxe version doll-B. Each doll of type B takes twice as long to produce as one of type A, and the company would have time to make maximum of 1000 per day. The supply of plastic is sufficient to produce 1000 dolls per day (both A & B combined). The deluxe version requires...
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Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the... highest profit. Use the corner point graphical approach. Let X1 = the number of air conditioners scheduled to be produced X2 = the number of fans scheduled to be produced Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity constraint) | | 2X1 | + | X2 | ≤ | 140 | (drilling capacity constraint) | |...
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fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs... $100 and provides an annual rate of return of 4%. The client wants to minimise risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis’s risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk...
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Julia’s Food Booth Case Problem Assignment 3 Max Z =Profit1x1+ Profit2x2+ Profit3x3 A - Formulation of the LP model... x1 - number of pizza slice x2 - number of hot dogs x3 - number of barbecue sandwiches Constraints Cost Maximum fund available for food = $1500 Cost per pizza $6 ÷08 (slices) = $0.75 Cost for a hot dog = $0.45 Cost for a barbecue sandwich = $0.90 Constraint: 0.75x1+0.45x2+0.90x3 ≤1500 Oven space Space available 16.3.4.2 = 384ft^2 384...
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Problem 4. (25 Points) Solve the following problem graphically (Please be neat). Draw the polytope on the x-y coordinate system... (can be done either by hand or computer). Show all intersection of the polytope and identify the point (x,y coordinate) where the objective function is maximized and provide that value. Maximize Z = 3x1 + 2x2 Subject to: 1x1 + 1x2 ≤ 10 8x1 + 1x2 ≤ 24 and x1, x2 ≥ 0 Solution : Point (a) is the origin (0,0) where Z(a) = 3*0 + 2*0 = 0 Point (b) is the...
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problem: n Maximize j=1 cjxj, subject to: n j=1 ai j x j = bi xj ≥ 0 x j integer (i = 1, 2, . . . , m), ( j =... 1, 2, . . . , n), (for some or all j = 1, 2, . . . , n). This problem is called the (linear) integer-programming problem. It is said to be a mixed integer program when some, but not all, variables are restricted to be integer, and is called a pure integer program when all decision variables must be integers. As we saw in the preceding chapter, if the constraints are of a network...
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Planning and Analysis: From Product Development through Use Kelton, Sadowski, and Sadowski Simulation with ARENA Khalil Management of... Technology Kolarik Creating Quality: Concepts, Systems, Strategies, and Tools Creating Quality: Process Design for Results Law and Kelton Simulation Modeling and Analysis Nash and Sofer Linear and Nonlinear Programming Nelson Stochastic Modeling: Analysis and Simulation Niebel and Freivalds Methods, Standards, and Work Design Pegden Introduction to Simulation...
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Chap 2 Linear Programming Models: Graphical and Computer Methods Lectured by Dr. TANG Huajun ( 唐華軍 ) Assistant Professor Office Address: A412... E-mail: hjtang@must.edu.mo 05/05/15 COB 207-Decision Methods 1 Steps in Developing a Linear Programming (LP) Model 1) Formulation: The process by which each aspect of a problem scenario is translated and expressed in terms of simple mathematical expressions. The aim is to ensure that the set mathematical equations, taken together, completely addresses...
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7) The branch and bound method can only be used for maximization integer programming problems. Answer: FALSE Diff: 1 Page Ref:... 187 Main Heading: Integer Programming Models Key words: integer programming models, branch and bound 8) The branch and bound solution method cannot be applied only to 0-1 integer programming problems. Answer: FALSE Diff: 2 Page Ref: 187 Main Heading: Integer Programming Models Key words: integer programming models, branch and bound method 9) In a problem...
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1. Discuss why and how you would use a liner programming model for a project of your choice, either from your own work or as a hypothetical... situation. Be sure that you stae your situation first, before you develpp the LP model Linear programming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps: Formulation Solution Interpretation ...
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Management science methods J.E. Beasley MN3032, 2790032 2011 Undergraduate study in Economics, Management, Finance and the Social... Sciences This subject guide is for a Level 3 course (also known as a ‘300 course’) offered as part of the University of London International Programmes in Economics, Management, Finance and the Social Sciences. This is equivalent to Level 6 within the Framework for Higher Education Qualifications in England, Wales and Northern Ireland (FHEQ). For more information...
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and solve a linear programming model for Julia that will help you advise her if she should lease the booth. Let, X1 =No... of pizza slices, X2 =No of hot dogs, X3 = barbeque sandwiches Formulation: 1. Calculating Objective function co-efficients: The objective is to Maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price. • For Pizza slice, Cost/slice=$6/8=$0.75 | |X1 ...
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required in solving LPPs by graphic method? Discuss in brief. 13) What is feasible region? Is it necessary that it should always be a convex... set? 14) Define iso-profit line. How does it affect the optimal solutions to an LPP? 15) How would you know whether the solution to a LPP is unique or not? In this connection, state the conditions that should be satisfied for more than one optimal solution. 16) Explain the phenomenon of ‘infeasibility’ in an LP problem. What are the indicators of...
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In the following expression, which is (are) the dependent variable(s)? PROFIT = REVENUE – EXPENSES. Profit The categories of modeling... techniques presented in this book include all of the following except: preventive models. Which of the following categories of modeling techniques includes optimization techniques? Prescriptive models What is the goal in optimization? Find the decision variable values that result in the best objective function and satisfy all constraints. The following linear...
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(a) Let x1=Number of Hot Dogs produced per week x2= Number of Hot Dog Buns produced per week z=Total profit per week... Number of employees=5 (40 hours each) Hence total amount of full time wok per week=5*40*60=12000 min Max z=0.8*x1 +0.3*x2 Subject to Constraints: 0.1*x1<=200 0.25*x2<=800 3*x1+2*x2<=12000 x1>=0, x2>=0 (b) Graphical method to solve the problem Using IOR tutorials (fig below) From the above LP model intercepts are: x1=2000 x2=3200 x1=4000,x2=6000 ...
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The simplex method is used regularly on applied problem involving thousands of variables and problem constrains (Barnett, Ziegler, & Byleen,... 2011). This was the method chosen when Wintel Technologies needed to figure out the best way to utilize time and schedule for their field engineers. With a busy schedule and being needed on several different areas in the United States, the simplex method was brought in to decide where and when employees should be spending their time and the company’s money....
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SENSITIVITY ANALYSIS The solution obtained by simplex or graphical method of LP is based on deterministic assumptions i.e. we... assume complete certainty in the data and the relationships of a problem namely prices are fixed, resources known, time needed to produce a unit exactly etc. However in the real world, conditions are seldom static i.e. they are dynamic. How can such discrepancy be handled? For example if a firm realizes that profit per unit is not Rs 5 as estimated but instead closer...
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Mat 540 Quiz 3 Question 1 .2 out of 2 points Correct The following inequality represents a resource constraint for a... maximization problem: X + Y ≥ 20 Answer Selected Answer: False Correct Answer: False Question 2 .2 out of 2 points Correct Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer Selected Answer: True Correct Answer: True Question 3 .2 out of 2 points Correct Surplus variables are only associated...
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12:01 PM Page 115 9 C H A P T E R Linear Programming: The Simplex Method TEACHING SUGGESTIONS Teaching Suggestion 9.1: Meaning... of Slack Variables. Slack variables have an important physical interpretation and represent a valuable commodity, such as unused labor, machine time, money, space, and so forth. Teaching Suggestion 9.2: Initial Solutions to LP Problems. Explain that all initial solutions begin with X1 ϭ 0, X2 ϭ 0 (that is, the real variables set to zero), and the slacks are...
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and make better estimates of what will happen in the future; this is the main purpose of forecasting. Some firms use subjective... methods, seat-of-the pants methods, intuition, and experience. There are also several quantitative techniques, moving averages, exponential smoothing, trend projections, and least squares regression analysis. Eight steps to forecasting: * Determine the use of the forecast—what objective are we trying to obtain? * Select the items or quantities that are to be forecasted...
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Calculate Basic Feasible Solution using Simplex Method Abstract: The problem of maximization/minimization deals with choosing the ideal set... of values of variables in order to find the extrema of an equation subject to constraints. The simplex method is one of the fundamental methods of calculating the Basic Feasible Solution (BFS) of a maximization/minimization. This algorithm implements the simplex method to allow for quick calculation of the BFS to maximize profit or minimize loss, depending on the...
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graphical method of solving a LPP involving two variables.[ 5 marks] 3. a. Explain the simplex procedure to solve a linear... programming problem. [ 5 marks] b. Explain the use of artificial variables in L.P [ 5 marks] 4. a. Explain the economic interpretation of dual variables. [ 5 marks] b. Define: Primal Problem and Dual Problem.[ 5 marks] 5. Describe the North-West Corner rule for finding the initial basic feasible solution in the transportation problem? [ 10 marks] 6. Use the simplex...
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USING STEPPING STONE AND MODI METHODS TO SOLVE TRANSPORTATION PROBLEMS BY ABDUSSALAM MUHAMMAD MUSTAPHA 09/211306009... A SEMINAR PAPER PRESENTED TO THE DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, USMANU DANFODIYO UNIVERSITY, SOKOTO IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF MASTER OF SCIENCE (MATHEMATICS) SUPERVISORY TEAM: MAJOR SUPERVISOR: DR. U. A. ALI CO – SUPERVISOR I: DR. I. J. UWANTA CO – SUPERVISOR II: DR. MU’AZU MUSA DATE: 07TH NOVEMBER...
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Simplex Methods of Linear Programming The graphical method is the more popular method to use because... they are easy to use and understand. Working with only a few variables at a time they allow operations managers to compare projected demand to existing capacity. The graphical method is a trial and error approach that can be easily done by a manager or even a clerical staff. Since it is trial and error though, it does not necessarily generate the optimal plan. One downside of this method though is...
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programming: 1. Linear Programming- involves no more than 2 variables, linear programming problems can be structured to minimize costs as well as... maximize profits. Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult. Linear programming is a useful technique to solve such problems. The necessary condition is that the data must be expressed in quantitative terms in the form of linear equations and inequalities...
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Bharathiar University Coimbatore-641046 CONTENTS Page No. Unit -I Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Quantitative Techniques – Introduction... Measures of Central Tendency Mathematical Model Linear Programming: Graphical Method Linear Programming: Simplex Method Unit -II Lesson 6 Lesson 7 Transportation Model Assignment Model 167 209 7 24 110 119 143 Unit -III Lesson 8 Lesson 9 Network Model Waiting Model (Queuing Theory) Unit -IV Lesson 10 Lesson 11 Lesson 12 Probability Theoretical Probability...
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the Theory of Constraints? The Theory of Constraints is an organizational change method that is focused on profit... improvement. The essential concept of TOC is that every organization must have at least one constraint. A constraint is any factor that limits the organization from getting more of whatever it strives for, which is usually profit. The Goal focuses on constraints as bottleneck processes in a job-shop manufacturing organization. However, many non-manufacturing constraints exist, such as...
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the stepping-stone method is that if, at a particular iteration, we accidentally choose a route that is not the best, the only penalty is to... perform additional iterations. 4) The transportation algorithm can be used to solve both minimization problems and maximization problems. 5) In the assignment problem, the costs for a dummy row will be equal to the lowest cost of the column for each respective cell in that row. Multiple Choice Questions: 6) Which of the following techniques can be...
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QUIZ LP Formulation 1. ACME Co. is a manufacturer of X’s which they sell to OR/MS teachers to be used as variables. For this week they... intend to manufacture two types of X’s, namely, X1’s & X2’s. The profit contribution for each unit of X1 & X2 are $4 and $5, respectively. Mr. Loony, the manager of ACME, found out that his available supply of raw material 1 (RM1) and raw material 2 (RM2) are 18 units and 24, respectively. Each unit of X1 will require 3 units of RM1 and 3 units of RM2 while...
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of interior and exterior paints that maximizes the daily profit. TAHA Example 2.1-1 (Page 47) : The Reddy Mikks Company LP... models have three basic components (like all OR models) – 1. 2. 3. Decision variables that we seek to determine. An objective that we need to optimize (minimize or maximize). This involves constructing an objective function. Constraints that the solution must satisfy. The variables of the model for solving this problem are : x1 = Tons of exterior paint to be produced...
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increase the capacity during the month. From the above, the group would want to address the following issues: a. What recommendations should... Ron Garcia make in order to address the over-booking problem of Mexicana? b. Is there a need for temporary workers to be re-hired in the drawing department? c. Does the plant lay-out of Mexicana optimize its production capacity? Case facts, limitations and constraints The data provided to Ron Garcia are as follows: April orders: Product Product W0075C Product...
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ADM2302 M, N, P and Q Solutions Assignment # 1 Assignment #1 Linear Programming Formulation, Graphical Method and Excel Solver Solution and... Marking Scheme 20 points After inputting the final grade on the 1st page, if the statement of integrity is not available or not signed by the given student (e.g. a team of three, two signed but the third did not) then deduct 2 marks. Show the “original grade” – 2 = “new grade”. 1. Please don’t forget to show the grade subtracted next to each mistake and show...
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Booth" Mat540 Quantitative Methods August 22, 2012 Julia’s Food Booth (A) Formulate and solve a L.P. model for this... case. Variables: Pizza - X1 $1.33 $1.50 14 inches Hot Dogs - X2 $0.45 $1.50 16 square inches Barbecue - X3 $0.90 $2.25 25 square inches Maximize Z= $0.75x1, 1.05x2, 1.35x3 Subject to: $0.75x1 + $0.45x2 + $0.90x3 ≤ $1,500 24x1 + 16x2 + 25x3 ≤ 55,296 in2 of oven space x1 ≥ x2 + x3 (changed to –x1 + x2 + x3 ≤ 0 for constraint) x2/x3 ≥ 2 (changed to –x2...
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on times when demand is low due to the fixed costs of the company. Probability of a favorable market is 60%. The company has a few couple of choices in the... plans for expanding the company, and after some deliberation, they have come up with the following decisions: 1) Expand with a Large Factory, having an estimate increase in income of P11,000 on a good demand and a loss of P1000 on a bad demand. 2) Expand with a Medium Factory, having an estimate increase in income of P8,000 on a good demand and...
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penalty has to be paid to the power plant. In this study, the objective is to match the calorific values required by the power plant. The quality features... and production capacities of coal from different panels are determined and are used in quality constraints. The power plant requires coal in two groups, which are of different qualities and quantities. Therefore, two linear programming models complementing each other are developed in order to determine the blending conditions that satisfy the needs of...
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Linear Programming Key Terms, Concepts, & Methods for the User Notes for Chemical Engineering 4G03 Thomas Marlin McMaster University... Hamilton, Ontario, Canada Copyright © 2002, 2003 by Thomas Marlin, Hamilton, Ontario, Canada Forward This material has been prepared for the student who wishes to learn the basic concepts about linear programming. The material will prepare the student to use linear programming in engineering practice. It should also provide a basis for further study...
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540- Quantitative Methods February 23, 2013 (A) Formulate and solve an L.P. model for this case. The... following variables were be used: X1 = Slices of Pizza X2 = Hot Dogs X3 = BBQ Sandwiches The objective is to maximize profit. maximize Z= 0 .75X1+1.05X2+1.35X3 Subject to: 0.75X1+1.05X2+1.35X3≤1,500 (Budget) 24X1+16X2+25X3≤55,296in2 (Oven Space) X1≥X2+X3 X2X3≥2.0 X1, X2, X3≥0 (B) Evaluate the prospect of borrowing money before the first game. Following table shows the sensitivity...
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LINEAR PROGRAMMING TERMINOLOGY The following is an alphabetical listing of various linear programming terms to be used throughout the... various LP topics: Active Constraint A constraint for which, when evaluated at optimality, the left-hand side equals the right-hand side. Graphically, this corresponds to a constraint line on which the optimal solution lies. Also called binding constraint. Allowable Ranges Sensitivity analysis provides information regarding the allowable ranges for certain...
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