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Linear programming 1 Basics - MIT Mathematics

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Lecture notesMarch 17, 2015Linear 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.

here is the data corresponding to a civilization with just two types of grains (G1 and G2) and three types of nutrients (starch, proteins, vitamins): Starch Proteins Vitamins Cost ($/kg) G1 5 4 2 0.6 G2 7 2 1 0.35 Nutrient content and cost per kg of food. The requirement per day of starch, proteins and vitamins is 8, 15 and 3 respectively. The ...

  Programming, Linear programming, Linear, Civilization

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