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In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P {\displaystyle P} and a vector x ∗ ∈ R n {\displaystyle \mathbf {x} ^{*}\in \mathbb {R} ^{n}} , x ∗ {\displaystyle \mathbf {x} ^{*}} is a ...
For example, if is non-basic and its coefficient in is positive, then increasing it above 0 may make larger. If it is possible to do so without violating other constraints, then the increased variable becomes basic (it "enters the basis"), while some basic variable is decreased to 0 to keep the equality constraints and thus becomes non-basic ...
Making a saline water solution by dissolving table salt in water.The salt is the solute and the water the solvent. In chemistry, a solution is defined by IUPAC as "A liquid or solid phase containing more than one substance, when for convenience one (or more) substance, which is called the solvent, is treated differently from the other substances, which are called solutes.
The possible results of Phase I are either that a basic feasible solution is found or that the feasible region is empty. In the latter case the linear program is called infeasible. In the second step, Phase II, the simplex algorithm is applied using the basic feasible solution found in Phase I as a starting point.
However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).
The difference between a basic salt and an alkali is that an alkali is the soluble hydroxide compound of an alkali metal or an alkaline earth metal. A basic salt is any salt that hydrolyzes to form a basic solution. Another definition of a basic salt would be a salt that contains amounts of both hydroxide and other anions. White lead is an ...
For example, in liquid ammonia, NH 2 − is the basic ion species which accepts protons from NH 4 +, the acidic species in this solvent. G. N. Lewis realized that water, ammonia, and other bases can form a bond with a proton due to the unshared pair of electrons that the bases possess. [ 3 ]
In chemistry, an alkali (/ ˈ æ l k ə l aɪ /; from the Arabic word al-qāly, القلوي) is a basic, ionic salt of an alkali metal or an alkaline earth metal. An alkali can also be defined as a base that dissolves in water. A solution of a soluble base has a pH greater than 7.0.