LINEAR PROGRAMMING II 1 Linear Programming II: Minimization © 2006 Samuel L. Baker Assignment 11 is on page 16. Introduction A minimization problem minimizes the value of the objective function rather than maximizing it. Minimization problems generally involve finding the least-cost way to meet a set of requirements. Classic example -- feeding farm animals. Animals need: 14 units of nutrient A, 12 units of nutrient B, and 18 units of nutrient C. Learning Objective 1: Recognize problems that
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Linear Programming (LP) Linear programming, simply put, is the most widely used mathematical programming technique. It has a long history dating back to the 1930s. The Russian mathematical economist Leonid Kantorovich published an important article about linear programming in 1939. George Stigler published his famous diet problem in 1945 (“The Cost of Subsistence”). Of course, no one could actually solve these problems until George Dantzig developed the simplex method, which was published in 1951
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Linear programming solution examples Linear programming example 1997 UG exam A company makes two products (X and Y) using two machines (A and B). Each unit of X that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B. Each unit of Y that is produced requires 24 minutes processing time on machine A and 33 minutes processing time on machine B. At the start of the current week there are 30 units of X and 90 units of Y in stock. Available processing
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METHODS/ APPROACH This scheduling problem can be solved most expeditiously using linear programming. Let F denote the number of full-time employ- ees. Some number, F1, of them will work one hour of overtime between 5 PM and 6 PM each day and some number, F2, of the full- time employees will work overtime between 6 PM and 7 PM. There will be seven sets of part-time employees who begin their work day at hour j=j␣1,2,...,7,withP1beingthenumberofworkers beginning at 9 AM, P2 at 10 AM, . . . , P7 at
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then X2=288 (0, 288) If x2 in equation (4) = 0, then X1 = 288 (288, 0) Due to the multiple constraints, it is difficult to obtain the optimal solution from the graph. Therefore, the simultaneous equation would be used to the solve linear programming model. Using simultaneous equation, 8x1 + 6x2 = 1920 ounces…………………………. (1) 3x1 + 6x2 = 1440 ounces…………………………. (2) 3x1 + 2x2 = 720 ounces…………………………… (3) X1 + x2 =288 jars………………………………….. (4) Using the
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LINEAR PROGRAMING AND SIMPLEX METHOD Devharajan Rangarajan Department of Electronic Engineering National University of Ireland, Maynooth devharajan.rangarajan.2016@mumail.ie Abstract— An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This pays way to a new world of constrained optimization. This paper focuses on one such optimization technique known
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Linear Programming: Using Solver in Excel Linear Programming was conceptually developed before World War II by the outstanding Russian mathematician A.N.Kolmogorov and gained its popularity ever since the development of Simplex method by George B. Dantzig in 1947. Linear programming deals with problems of maximizing or minimizing a linear function in the presence of linear equality and/or inequality constraints. In these problems, we find the optimal, or most efficient way of using limited resources
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The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4600 ounces of salt, 9400 ounces of flour, and 2200 ounces of herbs. A bag of Lime chips requires 1.5 ounces of salt, 5 ounces of flour, and 2 ounces of herbs to produce; while a bag of Vinegar chips requires 4 ounces of salt, 6 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.48,
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The development of linear programming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linear programming uses a mathematical model to describe the problem of concern. Linear programming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical
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LINEAR PROGRAMMING Definition. A mathematical technique for solving constrained maximization and minimization problems when there are many constraints and the objective function to be optimized, as well as the constraints faced, are linear (i.e., can be represented by straight lines) Assumptions. -LP is based on the assumption that the objective function that the organization seeks to optimize (maximize or minimize), as well as the constraints that it faces, are linear and can be represented
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