Preview

Linear Programming

Good Essays
Open Document
Open Document
1396 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
Linear Programming
QUANTITAVE TECHNIQUES OF BUSINESS ASSIGNMENT NO; 5 SUBMITTED TO; PROF. ADNAN SUBMITTED BY; NIDA WASIF ROLL # 54 MC-B TOPIC; LINEAR PROGRAMMING DATE; 5 JUNE, 14

UNIVERSITY OF CENTRAL PUNJAB

INTRODUCTION TO LINEAR PROGRAMMING

Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming. It is a mathematical technique used in computer modeling to find the best possible solution in allocating limited resources (energy, materials, machines, money etc) to achieve maximum profit or minimum cost. Linear Programming is a method of expressing and optimizing a business problem with a mathematical model. It is one of the most powerful and widespread business optimization tools. Linear programming can be used in very large variety of business problems. They include: transportation distribution problems production scheduling in oil & gas, manufacturing, chemical, etc industries financial and tax planning human resource planning facility planning fleet scheduling.

LINEAR PROGRAMMING; an optimization technique capable of solving an amazingly large variety of business problems. A business objective, business restrictions, and costs/revenue are formulated into a mathematical model. Algorithms for finding the best solutions are used. The concept behind a linear programming problem is simple. It consists for four basic components:
Decision variables
Continue Reading
View Writing Issues

You May Also Find These Documents Helpful

  • Satisfactory Essays

    OPRE/411 Week 4
    • 379 Words
    • 2 Pages

    OPRE/411 Week 4

    1. Use Solver in EXCEL to solve each of the following linear programming problems. To do so,…

    • 379 Words
    • 2 Pages
    Satisfactory Essays
    Read More
  • Satisfactory Essays

    Busn312 Hw3A
    • 727 Words
    • 3 Pages

    Busn312 Hw3A

    Linear programming problems have a.|linear objective functions, non-linear constraints.| b.|non-linear objective functions, non-linear constraints.| c.|non-linear objective functions, linear constraints.| d.|linear objective functions, linear constraints.| ____C 7. The first step in formulating a linear programming problem is a.|Identify any upper or lower bounds on the decision variables.| b.|State the constraints as linear combinations of the decision variables.| c.|Understand the problem.| d.|Identify the decision variables.| e.|State the objective…

    • 727 Words
    • 3 Pages
    Satisfactory Essays
    Read More
  • Powerful Essays

    Freaudian Analysis
    • 3380 Words
    • 14 Pages

    Freaudian Analysis

    1. Consider the following linear programming problem: Maximize Z = 400 x + 100y Subject to 8 x + 10y ≤ 80 2 x + 6y ≤ 36 x≤ 6 x, y ≥ 0…

    • 3380 Words
    • 14 Pages
    Powerful Essays
    Read More
  • Better Essays

    Acme
    • 1450 Words
    • 8 Pages

    Acme

    Linear programming is the “several related mathematical techniques used to allocate limited resources among competing demands in an optimal way” (Jacobs & Chase, 2013, appendix…

    • 1450 Words
    • 8 Pages
    Better Essays
    Read More
  • Good Essays

    Week 8 Assignment 1
    • 783 Words
    • 8 Pages

    Week 8 Assignment 1

    We are asked to formulate and solve the linear program in excel, write the sensitivity ranges for…

    • 783 Words
    • 8 Pages
    Good Essays
    Read More
  • Satisfactory Essays

    Mat 540 Quiz 4
    • 1474 Words
    • 6 Pages

    Mat 540 Quiz 4

    The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign…

    • 1474 Words
    • 6 Pages
    Satisfactory Essays
    Read More
  • Satisfactory Essays

    Quiz 4
    • 1484 Words
    • 11 Pages

    Quiz 4

    In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.…

    • 1484 Words
    • 11 Pages
    Satisfactory Essays
    Read More
  • Good Essays

    Mat 540 Week 9 Discussion
    • 374 Words
    • 2 Pages

    Mat 540 Week 9 Discussion

    Integer programming is concerned with optimization problems in which some of the variables are required to take on discrete values. Rather than allow a variable to assume all real values in a given range, only predetermined discrete values within the range are permitted. In most cases, these values are the integers, giving rise to the name of this class of models. Models with integer variables are very useful. Situations that cannot be modeled by linear programming are easily handled by integer programming. Primary among these involve binary decisions such as yes-no, build-no build or invest-not invest. Although one can model a binary decision in linear programming with a variable that ranges between 0 and 1, there is nothing that keeps the solution from obtaining a fractional value such as 0.5, hardly acceptable to a decision maker. Integer programming requires such a variable to be either 0 or 1, but not in-between. Unfortunately integer programming models of practical size are often very difficult or impossible to solve. Linear programming methods can solve problems orders of magnitude larger than integer programming methods. A typical mathematical program consists of a single objective function, representing either a profit to be maximized or a cost to be minimized, and a set of constraints that circumscribe the decision variables. In the case of a linear program (LP) the objective function and constraints are all linear functions of the decision variables. At first glance these restrictions would seem to limit the scope of the LP model, but this is hardly the case. Because of its simplicity, software has been developed that is capable of solving problems containing millions of variables and tens of thousands of constraints.…

    • 374 Words
    • 2 Pages
    Good Essays
    Read More
  • Satisfactory Essays

    Julia Booth
    • 404 Words
    • 2 Pages

    Julia Booth

    In this case study, I must create a linear programming model for Julia that will help her to decide whether or not she need to lease a booth. The three products or variable we must consider for this booth are pizza, hotdogs, and barbecue sandwiches. In this model, x 1 equal the number of pizza slices Julia should purchase, x2 equals the number of hotdogs Julia should purchase, and x3 equal the number of barbecue sandwiches Julia should purchase. The objective is to maximize total profit and the way to do that is to calculate each variable by subtracting cost from the selling price. For instance, if the pizza cost six dollar for eight slices then that mean she is only paying seventy-five cent for pizza and to make her money back she need to sell them for $1.50.…

    • 404 Words
    • 2 Pages
    Satisfactory Essays
    Read More
  • Good Essays

    MATH%$)
    • 535 Words
    • 4 Pages

    MATH%$)

    4. If a maximization linear programming problem consist of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ______ result in a(n) _____ solution to the integer linear programming problem.…

    • 535 Words
    • 4 Pages
    Good Essays
    Read More
  • Satisfactory Essays

    Multidisciplinary/Liberal Arts
    • 501 Words
    • 3 Pages

    Multidisciplinary/Liberal Arts

    Linear programming, the ability to find the smallest or biggest possible value under some constraints, is used in a typical optimization problem. In business this method helps to optimize solutions for politics, transportation scheduling, hospital stuffing, purchasing and many other problems. In biotechnology the same equation is used to optimize cell-factories, enabling the production of drugs, plastics, or any desired products.…

    • 501 Words
    • 3 Pages
    Satisfactory Essays
    Read More
  • Satisfactory Essays

    MAT 540 Week 6 Homework
    • 564 Words
    • 2 Pages

    MAT 540 Week 6 Homework

    6. The Pinewood Furniture Company produces chairs and tables from two resources – labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table requires 10 hours of labor and 6 board-ft. of wood. The profit derived from each chair is $400 and from each table, $100. The company wants to determine the number of chairs and tables to produce each day in order to maximize profit. Formulate a linear programming model for this problem.…

    • 564 Words
    • 2 Pages
    Satisfactory Essays
    Read More
  • Powerful Essays

    Chapter Summary of an Introduction to Management Science: Quantitative Approaches to Decision-Making
    • 4205 Words
    • 17 Pages

    Chapter Summary of an Introduction to Management Science: Quantitative Approaches to Decision-Making

    South-Western Cincinnati, Ohio Contents Preface Chapter 1: Introduction ♦ Scheduling a Golf League Chapter 2: An Introduction to Linear Programming ♦ Workload Balancing ♦ Production Strategy ♦ Hart Venture Capital Chapter 3: Linear Programming: Sensitivity Analysis and Interpretation of Solution ♦ Product Mix ♦ Investment Strategy ♦ Truck Leasing Strategy Chapter 4: Linear Programming Applications in Marketing, Finance and Operations Management ♦ Planning an Advertising Campaign ♦ Phoenix Computer ♦ Textile Mill Scheduling ♦ Workforce Scheduling ♦ Duke Energy Coal Allocation Chapter 6: Distribution and Network Models ♦ Solution Plus ♦ Distribution Systems Design Chapter 7: Integer Linear Programming ♦ Textbook Publishing ♦ Yeager National Bank ♦ Production Scheduling with Changeover Costs Chapter 8: Nonlinear Optimization Models ♦ Portfolio Optimization with Transaction Costs Chapter 9: Project Scheduling: PERT/CPM ♦ R.C. Coleman Chapter 10: Inventory Models ♦ Wagner Fabricating Company ♦ River City Fire Department Chapter 11: Waiting Line Models ♦ Regional Airlines ♦ Office Equipment, Inc.…

    • 4205 Words
    • 17 Pages
    Powerful Essays
    Read More
  • Satisfactory Essays

    Objective Function vs Constraints in Linear Programming
    • 435 Words
    • 2 Pages

    Objective Function vs Constraints in Linear Programming

    Linear Programming Model in Operation Research study is usually mathematical type of model which contains set of equations that represent objective function and constraints. The keywords in this article are Objective Function and Constraints, according to Heizer & Render (2008) Objective Function are mathematical expression expressed in linear programming designed to maximizes or minimizes some quantity, for example profit can maximized while the cost might be reduced. The objective function is also called effectiveness function, it is the mathematical expression of the objectives which may be cost of operation or profit on operation (Kumar and Hira, 2008). Constraints which is also known as restrictions are mathematical expressions of the limitations that are involved in fulfilling the objectives; they are caused by scarce or limited resources which may include money, space, manpower, materials and so on. Heizer & Render (2008) defined constraints as restrictions which limit the extent to which a manager can pursue an objective…

    • 435 Words
    • 2 Pages
    Satisfactory Essays
    Read More
  • Good Essays

    Linear Optimization
    • 1790 Words
    • 8 Pages

    Linear Optimization

    Linear optimization is a mathematical method for determining a way to achieve the best outcome such as maximum profit or lowest cost in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming…

    • 1790 Words
    • 8 Pages
    Good Essays
    Read More

Related Topics