Linear Programming Lab
Work through real-world optimization problems using the graphical method. Set up objective functions and constraints, visualize feasible regions, identify optimal solutions, and explore how changing parameters affects the answer.
Guided Experiment: Graphical Method
Where do you predict the optimal solution will be found: at a corner point, on an edge, or in the interior of the feasible region?
Write your hypothesis in the Lab Report panel, then click Next.
Feasible Region
Controls
Results
Corner Points
| x | y | Z |
|---|---|---|
| 3.00 | 1.50 | ★ 21.00 |
| 4.00 | 0.00 | 20.00 |
| 0.00 | 3.00 | 12.00 |
| 0.00 | 0.00 | 0.00 |
Data Table
(0 rows)| # | Problem | Constraints | Corner Pts | Optimal x | Optimal y | Optimal Z |
|---|
Reference Guide
LP Formulation
Every linear program has three parts: decision variables, an objective function, and constraints.
The objective coefficients represent profit, cost, or some other quantity to be maximized or minimized.
Graphical Method
For two-variable problems, the graphical method plots each constraint as a line and identifies the feasible region.
The optimal solution is found by evaluating the objective at each corner point of the feasible polygon.
Corner Point Theorem
If a linear program has an optimal solution, it occurs at a vertex (corner point) of the feasible region.
This theorem makes it possible to solve LP problems by checking a finite number of points.
Binding Constraints
A constraint is binding when it holds with equality at the optimal solution. Non-binding constraints have slack.
Only binding constraints affect the optimal value. Relaxing a non-binding constraint does not change the solution.
