NounWikipedia has an article on: Linear programminglinear programming (abbreviated as LP)
From Wiktionary under the GNU Free Documentation License. Linear programming (LP) 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 equations. More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Given a polytope and a real-valued affine function defined on this polytope, a linear programming method will find a point on the polytope where this function has the smallest (or largest) value if such point exists, by searching through the polytope vertices. Linear programs are problems that can be expressed in canonical form:
where x represents the vector of variables (to be determined), c and b are vectors of (known) coefficients and A is a (known) matrix of coefficients. The expression to be maximized or minimized is called the objective function (cx in this case). The equations Ax ≤ b are the constraints which specify a convex polytope over which the objective function is to be optimized. (In this context, two vectors are comparable when every entry in one is less-than or equal-to the corresponding entry in the other. Otherwise, they are incomparable.) Linear programming can be applied to various fields of study. It is used most extensively in business and economics, but can also be utilized for some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design. From Wikipedia under the
GNU Free Documentation License How could I teach linear programming to my classmates in a creative way? Q. So that my project could be a success, I need to be able to get them interested in linear programming, done in a unique way. Any suggestions? Asked by mozzarella_24 - Sat Jan 20 18:52:40 2007 - - 2 Answers - 0 Comments A. Ummm ... use your classmates as the variables and constraints? I mean ... set up your presentation/problem the way you are going to ... write out on index cards (one variable or one constraint per card per person) to give to each classmate (I'm not sure how many people in the class) so that they become the project in the form of being linear programming. Am I making sense? Just a thought ... use the people in the class to present LP in a kinesthetic really involved way ... so that they in essence become the presentation while simultaneously learning what you are presenting. Good luck ... hope this helps! Answered by mehs - Sat Jan 20 19:55:49 2007 How to formulate proportionality of two vectors by mixed integer linear programming (MILP)? Q. I need to add some constraint(s) to my "mixed integer linear program" to check if two vectors are proportional. How can I formulate this? I need to add some constraint(s) to my "mixed integer linear program" to check if two vectors are proportional. How can I formulate this? I should add that the vectors are the variables. Asked by Amir - Sat Mar 6 02:43:56 2010 - - 2 Answers - 0 Comments A. Let's say you want to know if vector Answered by Hal Roach - Sat Mar 13 22:05:23 2010 Can you give me the equations for this linear programming problem?
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