A Linear Problem is made of an objective function( a linear function of some variable) , a set of constraint on variables and the range of the variable.
Here is an example a linear problem
We have two useful formulations: Standard and canonical.
Stantard formulation
This formulation use one Matrix A and two vectors b and c.
Matrix A is made of the coefficients of the variables in the set of constraints.
c is made of coefficients of the variable in the objective function.
b is made of the values on the right side of the constraints equations.
Canonical Formulation
This formulation is derived from the previous one and use two matrix B and D and two vectors b and c.
This is always true: A = B | D.
B is the first part of the matrix A and is made of basic variable. D is the second part and of course is made of the non basic variables. This image show how to go from the standard form to the canonical one.
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Example of some Linear Programming Problem in Standard Form
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