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Linear Programming

Linear programming is a way to determine the best outcome in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is specific case of mathematical programming. Linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. A linear programming algorithm finds a point in the polyhedron where this function has the smallest value if such point exists.

Linear programming can be applied to various fields of study. It is used in business and economics but is also utilized in engineering applications. Some industries that utilize linear programming models include transportation energy telecommunications and manufacturing. Many practical problems in operation research can be expressed as linear programming problems.

Standard form is the typical form of describing a linear programming problem. This form consists of three parts that are shown below:

A linear function to be maximized

F(x1, x2) = c1x1 + c2x2

Problem constraints

A11x1 + a12x2 <= b1

A21x1 + a22x2 <= b2

A31x1 + a32x2 <= b3

Non negative variables

X1>= 0

X2>= 0

The problem is usually expressed in matrix form and therefor becomes:

Ma{cTx| Ax <= b ^ x >= 0}

Categories within Linear Programming


Postings: 404

Optimization is the selection of a best element from some set of available alternatives.

Investment Strategy Case Problem

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Network Optimization Problem

A utility company serves three cities from its three power plants. The power plant capacities and energy delivery costs per unit (in $) from each plant to each city are as follows in the attached document. 1. Draw the network representation for this problem. 2. Formulate the linear program to minimize total cost of energy

Linear programming using two-phase simplex and graphical method

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Linear Programming Using the M-technique

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LP Scheduling problem

A nursing home employs attendants who are needed around the clock. Each attendant is paid the same, regardless of when his or her shift begins. Each shift is 8 consecutive hours. Shift begin at 6 a.m., 10 am, 2 pm, 6 pm, 10 pm and 2 am. The following table shows the nursing home's requirements for the numbers of attendants to be

Using Excel Solver to Maximize Profit for a Cargo Ship

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Integer Programming - Linear Programming

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Linear Integer Programming: Integer Values

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Solving Linear Programming in Excel Solver-Maximization

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Linear Transformation - Sensitivity Analysis

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Integer Programming Problem: Transportation and Transshipment

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Applications of Linear Programming

Linear Programming Scenario # 1 A new woodworking company is going to manufacture and sell dining room tables and chairs. The company's owner has assumed that his customers are interested in buying tables and chairs individually, rather than having to buy them in predetermined sets, as is the case with his competitors. T

Linear Programming - Transportation Problem, North West corner

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Transformation Algorithms - Linear Programming Models

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Determining Optimal Ranges

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Linear Programming Model to Determine Amount of Projects For Texmart To Undertake

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Model Linear Program for a car manufacturer

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Linear Programming: The Lancaster Decor Company

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Linear Programming: Toasties by Ajax Corp

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Linear Programming for Weinberger Electronics

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Nonlinear Programming Model

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Linear Programming: Hart Manufacturing

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Linear programming model for revenue management application

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Linear Programming and Using Solver

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Linear Programming: Feed N' Ship Ranch

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Chain Restaurant Problem: Linear Programming in Excel

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Linear Programming Formulations

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Questions in Linear Programming

Please review my answers highlighted in red for the linear programming questions Your feed back is requested on items I did correctly or incorrectly Thank you