Describe graphical and simplex method of solving lp problems?
Question: Describe graphical and simplex method of solving lp problems?
Linear programming (LP) is a technique for finding the optimal value of an objective function subject to a set of constraints. There are two main methods for solving LP problems: graphical and simplex.
The graphical method is a visual way of solving two-variable LP problems. It involves plotting the feasible region (the set of all possible solutions that satisfy the constraints) on a coordinate system, and then finding the optimal solution by moving along the objective function line. The graphical method is useful for understanding the basic concepts of LP, but it is not practical for problems with more than two variables.
The simplex method is an algebraic procedure that can handle any number of variables and constraints. It works by transforming the original problem into a standard form, and then applying a series of operations called pivoting to move from one basic feasible solution to another, until the optimal solution is reached. The simplex method is more efficient and reliable than the graphical method, but it requires more calculations and may encounter some difficulties such as degeneracy or unboundedness.
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