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The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [ 1] It is used most often to compare two numbers on the number line by their size.
Linear inequality. In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [ 1] < less than. > greater than. ≤ less than or equal to. ≥ greater than or equal to. ≠ not equal to.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
Farkas' lemma. In mathematics, Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas. [ 1] Farkas' lemma is the key result underpinning the linear programming duality and has played a central role in the development of mathematical optimization ...
The binary number system expresses any number as a sum of powers of 2, and denotes it as a sequence of 0 and 1, separated by a binary point, where 1 indicates a power of 2 that appears in the sum; the exponent is determined by the place of this 1: the nonnegative exponents are the rank of the 1 on the left of the point (starting from 0), and ...
Fourier–Motzkin elimination. Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier [ 1] who proposed the method in 1826 and Theodore Motzkin who re-discovered it in 1936.
Entitlement theory is a theory of distributive justice and private property created by Robert Nozick in chapters 7 and 8 of his book Anarchy, State, and Utopia.The theory is Nozick's attempt to describe "justice in holdings" (Nozick 1974:150)—or what can be said about and done with the property people own when viewed from a principle of justice.
Chebyshev's inequality. In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance) from its mean. More specifically, the probability that a random variable deviates from its mean by more than is at most ...