Linear Programming

Inequalities and the Feasible Region

Visualize linear constraints and the feasible region in optimization problems.

The Objective Function and Corner Points

Use geometry to identify optimal solutions at boundary corners.

High Dimensional Solvers

Scale linear programming solvers to higher dimensions and more constraints.

// Unit 2: Under the Hood (The Simplex Algorithm)

Standard Form and Slack Variables

Convert optimization problems into standard form with slack variables.

The Simplex Engine

Step through the simplex algorithm on linear programs.

Degeneracy and Edge Cases

Handle degenerate pivots and edge cases in simplex implementations.

// Unit 3: Duality and the Value of Resources

The Primal and the Dual

Interpret duality as pricing resources in optimization.

Shadow Prices & Marginal Value

Explore shadow prices and economic interpretations of dual variables.

The Diet Problem

Solve a classic diet optimization problem using linear programming.

// Unit 4: Network Optimization

The Transportation Problem

Solve transportation optimization problems with linear programming.

Maximum Flow

Use network flow models to compute maximum flow solutions.

The Assignment Problem

Match agents to tasks optimally using linear programming.

// Unit 5: Integer Programming

The Continuous Relaxation Trap

Explore how integer programs differ from relaxed linear programs.

Branch and Bound

Implement branch-and-bound search for integer optimization.

The Knapsack Problem & Binary IP

Solve knapsack-style integer programs with binary variables.