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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. A certain amount of each nutrient is required per day.

Linear Programming deals with the problem of optimizing a linear objective function subject to ... G2 7 2 1 0.35 Nutrient content and cost per kg of food. ... amount per day of each nutrient at minimal cost. When trying to formulate a problem as a linear program, the rst step is to decide which decision variables to use. These variables ...

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