An Economic Interpretation of Linear Programming by Quirino Paris

By Quirino Paris

This textual content covers the elemental concept and computation for mathematical modeling in linear programming. It offers a robust history on the way to manage mathematical proofs and high-level computation tools, and comprises titanic heritage fabric and course. Paris provides an intuitive and novel dialogue of what it capacity to unravel a procedure of equations that may be a the most important stepping stone for fixing any linear software. The dialogue of the simplex process for fixing linear courses offers an financial interpretation to each step of the simplex set of rules. The textual content combines in a special and novel approach the microeconomics of creation with the constitution of linear programming to offer scholars and students of economics a transparent inspiration of what it capacity, formulating a version of financial equilibrium and the computation of chance price within the presence of many outputs and inputs.

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T. prices prices (mrtt) ⎡ Dual: When executed, the production plan of the price taker will become his output supply of the produced commodities to the market of interest. 5 Why Another Linear Programming Book? ” What justifies another book on this subject? Two words: duality and symmetry. In many existing LP textbooks duality is not given a proper treatment. For economists, on the contrary, duality is the principal source of information about economic relations. The symmetry aspect of linear programming was clearly expounded in the pricetaking example.

The coefficients [ 6 1 ] constitute the technology for producing one unit of commodity corn. To perceptive readers it may seem that to go from a nonlinear production function (as in the usual economic theory courses) to a linear technology (as in linear programming ) entails a considerable loss of generality. There is no doubt that their perception is correct only to be substantially mitigated by the realization that with linear programming we can immediately deal with multiple outputs and multiple limiting (“fixed”) inputs without the complexities of a nonlinear mathematical specification.

Hence, if a solution seems implausible, linear programming approach should not be blamed, only its user. A detailed farm problem will be discussed in chapter 17. 9 A Second Encounter with Duality The story of a competitive firm is retold here as a reinforcement of the notions presented in previous sections. All problems possess a twofold representation that is customarily defined as duality. Duality is nothing else than the specification of one problem from two different points of view (any coin has two faces).

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