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A linear programming problem seeks to optimize (find a maximum or minimum value) a function (called the objective function) subject to a number of constraints on the variables which, in general, are linear inequalities. [6] The list of constraints is a system of linear inequalities.
Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 . Occasionally, chained notation is used with inequalities in different directions, in which case the meaning is the logical conjunction of the inequalities ...
NuCalc, also known as Graphing Calculator, is a computer software tool made by Pacific Tech. It can graph inequalities and vector fields, and functions in two, three, or four dimensions. It supports several different coordinate systems, and can solve equations. It runs on OS X as Graphing Calculator, and on Windows.
In addition to graphing both equations and inequalities, it also features lists, plots, regressions, interactive variables, graph restriction, simultaneous graphing, piecewise function graphing, recursive function graphing, polar function graphing, two types of graphing grids – among other computational features commonly found in a ...
Balinski's theorem states that the graph obtained in this way from any d-dimensional convex polytope is d-vertex-connected. [8] In the case of three-dimensional polyhedra, this property and planarity may be used to exactly characterize the graphs of polyhedra: Steinitz's theorem states that G is the skeleton of a three-dimensional polyhedron if ...
In general, a system with fewer equations than unknowns has infinitely many solutions, but it may have no solution. Such a system is known as an underdetermined system. In general, a system with the same number of equations and unknowns has a single unique solution. In general, a system with more equations than unknowns has no solution.
However, the elimination process results in a new system that possibly contains more inequalities than the original. Yet, often some of the inequalities in the reduced system are redundant. Redundancy may be implied by other inequalities or by inequalities in information theory (a.k.a. Shannon type inequalities).
Grapher is a graphing calculator capable of creating both 2D graphs including classic (linear-linear), polar coordinates, linear-logarithmic, log-log, and polar log, as well as 3D graphs including standard system, cylindrical system, and spherical system. Grapher is a Cocoa application which takes advantage of Mac OS X APIs.
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