What is a pivot/basic variable? Free variable?
A pivot/basic variable corresponds to a pivot column. A free variable corresponds to a solution of the system for any value.
In linear programming, a pivot variable (also known as a basic variable) is a variable that is part of the basic feasible solution that optimizes the objective function. Basic feasible solutions are those that satisfy all of the constraints of the problem and are identified by having a set of non-zero and linearly independent variables. By pivoting, or exchanging, the value of the pivot variable with another non-basic variable, the objective function can be improved until an optimal solution is found.
On the other hand, a free variable (also known as a non-basic variable) is a variable that is not part of the basic feasible solution and can take on any value without violating any of the constraints. Free variables do not affect the objective function and are often used to express the optimal solution in terms of variables that are convenient for interpretation.
To summarize, pivot/basic variables are part of the basic feasible solution that optimize the objective function, while free variables are not part of the basic feasible solution and can take any value without violating constraints.
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