A course for building intuition about 2-variable linear programming through diagrams, by repeatedly computing intercepts, intersections, objective values, and multiple optima by hand.
Step back and forth between diagrams and short practice problems to build up the ideas of linear programming one layer at a time. Each step — intercepts, feasibility checks, intersections, objective values, multiple optima — is something you compute by hand.
Grading and progress saving all happen inside the browser. No sign-up, no login, no install.
Right after reading the body text, compute intercepts, intersections, and objective values on the spot. Instead of saving everything for the end, you correct misunderstandings as soon as they appear.
By linking the diagram, the hand calculation, and the solver in that order, you can follow not just the answer but the reason the optimum comes out where it does.
Chapter 7 works through a separate case as a mixed review and lets you check your progress across all chapters in one place.
z = c_x x + c_y y (compute the objective value)a x + b y \le r (check whether a point satisfies a constraint)a_1 x + b_1 y = r_1 and a_2 x + b_2 y = r_2 simultaneously to find the intersectionz at every vertex and pick the largestBefore getting into the general theory of the simplex method or duality, the goal is to make sure you can carry out these four steps by hand.
Throughout the course we use a 2-variable LP for planning how much of product A and product B to make.
| Item | Content |
|---|---|
| Decision variables | x: number of lots of product A, y: number of lots of product B |
| Objective function | maximize z = 3x + 5y |
| Constraint 1 | 2x + y ≤ 16 (cutting stage) |
| Constraint 2 | x + 2y ≤ 14 (finishing stage) |
| Non-negativity | x ≥ 0, y ≥ 0 |
See why profit alone does not decide the plan, by computing process times.
Turn prose into equations and pin down what the coefficients and right-hand sides mean in numbers.
Find intercepts, check feasibility, and solve for intersections by hand to get a feel for the shape of the feasible region.
Evaluate the objective at each vertex to locate the optimum and recognize multiple optima.
Slide the coefficients and right-hand sides and watch in the simulator how the optimum switches from one vertex to another.
Follow the enumeration of vertex candidates and the feasibility check in a minimal reference implementation.
Work through a separate mixed-review case and review your progress chapter by chapter.
High-school linear functions and 2-by-2 systems of linear equations are enough. We do not use matrices, a proof of the simplex method, or duality.
When you see a 2-variable linear program, you should be able to explain which equations are constraints, which points are feasible, and why that particular vertex is optimal, using both diagrams and hand calculation.