Linear Pro-Linear Programming Problem Solver

Example

Linear Pro helps solve a linear programming problem where the objective is to maximize profit given constraints on resource availability. It guides the user through each iteration of the Simplex tableau, from introducing slack variables to identifying the pivot element, and calculating the next tableau.

Scenario

A manufacturing company wants to maximize production output while staying within limits of available labor and materials. Linear Pro assists in formulating and solving the LP problem to find the optimal production mix.

Example

Linear Pro explains when and how to introduce slack variables (for ≤ constraints), surplus variables (for ≥ constraints), and artificial variables (when necessary to ensure feasibility in Phase I of the Simplex method).

Scenario

A student working on a transportation problem with inequality constraints uses Linear Pro to understand how to incorporate slack variables to convert the constraints into equalities for use in the Simplex method.

Example

Once the final simplex tableau is reached, Linear Pro explains how to interpret the results, identifying the values of decision variables, the optimal value of the objective function, and checking if artificial variables are non-zero (which would indicate an infeasible solution).

Scenario

In a logistics optimization case, a user solves the LP problem with Linear Pro and needs to understand whether the solution is optimal and feasible. Linear Pro explains that if an artificial variable remains positive, the original problem has no feasible solution.

Example

Linear Pro walks users through converting a primal problem into its dual form, solving the dual using the simplex method, and then interpreting the results to provide insight into both the primal and dual problems.

Scenario

An economics student needs to solve a cost minimization problem (dual of a profit maximization problem). Linear Pro assists in formulating the dual, applying the simplex method, and interpreting the dual’s implications for the primal problem.

Example

Linear Pro explains important LP concepts like the Fundamental Theorem of Linear Programming, which guarantees that if an optimal solution exists, it will be found at a vertex of the feasible region.

Scenario

A student preparing for an exam wants to deepen their understanding of LP theory. Linear Pro provides insights into the theoretical underpinnings of the Simplex method and its guarantees regarding solution optimality and feasibility.