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Linear programming 1 Basics - MIT Mathematics

Lecture notesMarch 17, 2015 Linear programmingLecturer: Michel Goemans1 BasicsLinear Programmingdeals with the problem of optimizing a linearobjective functionsubject tolinear equality and inequalityconstraintson thedecision variables. Linear programming has manypractical applications (in transportation, production planning, ..). It is also the building block forcombinatorial optimization. One aspect of Linear programming which is often forgotten is the factthat it is also a useful proof technique. In this first chapter, we describe some Linear programmingformulationsfor some classical problems. We also show that Linear programs can be expressed in avariety of equivalent The Diet ProblemIn the diet model, a list of available foods is given together with the nutrient content and the costper unit weight of each food.

2 subject to: 5x 1 + 7x 2 8 4x 1 + 2x 2 15 2x 1 + x 2 3 x 1 0;x 2 0: Some more terminology. A solution x= (x 1;x 2) is said to be feasible with respect to the above linear program if it satis es all the above constraints. The set of feasible solutions is called the feasible space or feasible region. A feasible solution is optimal if its ...

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math.mit.edu

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math.mit.edu

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math.mit.edu

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math.mit.edu

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