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Linear Programming

In: Linear Algebra for Economists

Author

Listed:
  • Fuad Aleskerov

    (National Research University)

  • Hasan Ersel

    (Sabanci University)

  • Dmitri Piontkovski

    (National Research University)

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.

Suggested Citation

  • Fuad Aleskerov & Hasan Ersel & Dmitri Piontkovski, 2011. "Linear Programming," Springer Texts in Business and Economics, in: Linear Algebra for Economists, chapter 11, pages 195-216, Springer.
    • Handle: RePEc:spr:sptchp:978-3-642-20570-5_11
    DOI: 10.1007/978-3-642-20570-5_11
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