Solve variable linear programming problems

Variable Linear Programming Problems

Linear programming is a technique used to optimise a linear objective function subjected to a set of linear inequality or equality constraints.
A Variable Linear Programming Problem involves situations where the coefficients of the constraint equations can change.
Objective functions and constraints consist of linear equations or inequalities.

The Graphical solution method is feasible for problems with two variables. It involves plotting the constraints on a graph, identifying the feasible region, and finding the optimal solution along the vertices of this region.
The Simplex method solves more complex problems (three or more variables) by transforming the problem into a system of linear equations.

Define variables: Identify the decision variables that need to be determined.
Formulate the objective function: Determine the linear equation to be minimised or maximised.
Formulate constraints: Identify the restrictions or limitations as linear inequalities or equations.
Construct a graphical model (for 2-variable problems): Plot the constraints and identify the feasible region.
Identify optimal solutions: Find the point(s) that optimise the objective function, which occurs at the vertices of the feasible region for 2-variable problems.
Apply the Simplex method (for problems involving 3 or more variables).

Linear Programming has extensive use in various fields such as business, economics, and engineering.
It helps in resource allocation, production scheduling, and transportation scheduling.
The method is integral in operational research for optimising the use of time, energy, and resources.