Chapter 7 – Linear Programming S. Neuburger Linear Programming Linear programming is widely used in planning resource allocation. The most common type of application involves allocating limited resources among competing activities in a best (i.e. optimal) way.) Programming refers to modeling and solving a problem mathematically. Product mix problem is common application of LP to determine how much of each product a company should produce. Properties of LP problems: • Goal is to maximize or minimize some quantity, generally profit or cost, respectively. • Limiting constraints (restrictions). • There are alternative courses of action to choose from. • Linear equations and inequalities – variables are of first degree and only appear in one term of each equation. Assumptions of LP: • Certainty of quantities • Proportionality • Additivity – sum of all activities equals sum of individual activities • Divisibility – unlike integer programming • Nonnegativity of variables
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