# Linear Programming

Mtetwa, D. K. J. (David K. J.) (2010)

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This module introduces the learner to a particular mathematical approach to analysing real life activity that focuses on making specific decisions in constrained situations. The approach, called linear programming, is presented here with an emphasis on appreciation of the style of thinking and interpretation of mathematical statements generated, rather than on computational competency per se, which is left to appropriate and readily available ICT software package routines. The module begins with Unit One that consists of 2 main Activities. Activity 1, formulation of a linear programming problem, is on a mathematical description of the problematic situation under consideration, and Activity 2, the geometrical approach considers a visual description of a plausable solution to the problem situation. Unit 1 therefore should move the learner towards an appreciation of real-life activity situations that can be modelled as linear programming problems. With 3 main activities, Unit 2 considers computational algorithms for finding plausible optimal solutions to the linear programming problem situations of the type formulated in Unit 1. Activity 3 examines conditions for optimality of a solution, which is really about recognising when one is moving towards and arrives at a candidate and best solution. Activity 4 discusses the centre piece of computational algebraic methods of attack, the famed Simplex algorithm. This module focuses on the logic of the algorithm and the useful associated qualitative properties of duality, degeneracy, and efficiency. The final Activity touches on the problem of stability of obtained optimal solutions in relation to variations in specific input or output factors in the constraints and objective functions. This so called post optimality or sensitivity analysis is presented here only at the level of appreciation of the analytic strategies employed.

African Virtual University (AVU)

- Mathematics702