Linear Programming

Fuad Aleskerov, Hasan Ersel () and Dmitri Piontkovski
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Hasan Ersel: Sabanci University

Chapter 11 in Linear Algebra for Economists, 2011, pp 195-216 from Springer

Abstract: Abstract The linear programming problem is a general problem of finding the maximal value of the function f(x) = (a, x), where $$\mathbf{x} \in {\mathbb{R}}^{n}$$ is a vector of n unknowns and $$\mathbf{a} \in {\mathbb{R}}^{n}$$ is a constant vector, under the restrictions $$\mathbf{x} \geq \mathbf{0}\mbox{ and }A\mathbf{x} \geq \mathbf{d},$$ where A is a matrix and d is a constant vector. This problem has a lot of applications to economic models and practice. Some simple and rather artificial applications are discussed below. In mathematical terms the problem is maximizing a linear objective function under linear constraints where the relevant variables are restricted to be non-negative. It was first solved by Kantorovich.

Keywords: Dual Problem; Linear Programming Problem; Domestic Saving; Economic Unit; Linear Objective Function (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-642-20570-5_11

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DOI: 10.1007/978-3-642-20570-5_11

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