Explore interactive activities designed to support SIE 340. Select a topic, work through guided practice, and use the open-ended explorers to test your own examples. Each lab runs directly in your browser, no installation is required.
Practice essential linear algebra skills for operations research, including vectors, matrix operations, elementary row operations, reduced-row echelon form, Gauss–Jordan elimination, linear systems, and basic and nonbasic variables.
Practice translating real-world problems into linear programming models by identifying decision variables, objective functions, constraints, and sign restrictions.
Practice solving two-variable linear programs graphically by plotting constraint lines, identifying the feasible region and extreme points, and moving the objective line to locate the optimal solution.
After completing the practice problems, use the interactive lab linked below to enter your own coefficients, explore additional examples, and check your understanding step by step.
Practice solving linear programs using the simplex method by selecting entering and leaving variables, performing pivots, updating tableaus, and interpreting the optimal solution.
After completing the practice problems, use the interactive lab linked below to enter your own coefficients, explore additional examples, and check your understanding step by step.
Practice converting linear programming models into standard form by introducing slack, surplus, and artificial variables. Practice identifying decision variables, objective functions, constraints, and sign restrictions.
Simplex Outcomes and Special Cases
Practice interpreting simplex and Big M tableaus to identify unique optimal solutions, multiple optimal solutions, unbounded problems, infeasible problems, and degenerate basic feasible solutions. Use guided checkpoints to recognize the tableau conditions associated with each outcome.
Optimal Tableaus and Sensitivity Analysis
Practice constructing an optimal simplex tableau from a given basis and analyzing how changes to objective-function coefficients and constraint right-hand sides affect optimality, feasibility, the optimal solution, and the objective value.
Practice converting a primal linear program into its dual. Identify the dual variables, objective function, constraints, coefficient relationships, and sign restrictions for different primal formulations.
Duality Theorems and Optimality
Practice using weak and strong duality to establish objective bounds, certify optimal solutions, interpret the duality gap, connect unboundedness with infeasibility, and recover dual information from an optimal primal tableau.
Shadow Prices and Complementary Slackness
Practice interpreting shadow prices, updating the optimal objective value within allowable RHS ranges, applying complementary slackness, and using a known primal or dual solution to determine its optimal counterpart.
Learn how to interpret an optimal solution and sensitivity report produced by Excel Solver. Examine decision-variable values, binding constraints, slack, reduced costs, shadow prices, and allowable increases and decreases.