A tool designed for solving linear programming problems, particularly those where an initial basic feasible solution is not readily available, enables the systematic manipulation of constraints and variables. It first introduces artificial variables to transform the problem into a format where a feasible solution is apparent. For example, in a minimization problem with ‘greater than or equal to’ constraints, the tool adds artificial variables to these constraints to form an initial identity matrix, thereby establishing a starting feasible basis.
This approach offers a structured way to overcome the challenges associated with finding an initial feasible solution, crucial for many real-world optimization scenarios. Its development streamlined the process of tackling complex linear programming problems, removing the need for manual manipulation and guesswork in the preliminary stages. By automating the initial phase of problem setup, it reduces the potential for human error and accelerates the overall solution process.