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In [[applied mathematics]], '''linear-fractional programming (LFP)''' formally is almost the same as [[linear programming]] (LP) but instead of linear [[objective function]] one has a ratio of two linear functions, subject to linear constraints. Informally, if linear programming determines the way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model and given some list of requirements represented as linear equations, in linear-fractional programming model we can achieve the best (highest) ratio of outcome to cost, i.e. highest efficiency.
For example, if in the frame of LP we maximize '''profit = income − cost''' and obtain maximal profit of 100 units (= $1100 of income − 1000$ of cost), then using LFP we can obtain only $10 of profit which requires only $50 of investment. Thus, in LP we have efficiency $100/$1000 = 0.1, at the same time LFP provides efficiency equal to $10/$50 = 0.2.
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