Lesson 8.1 · 24 of 25 lessons
Constraints & vertices
Use constraint vertices and payoff matrices to explore optimization applications.
Open the interactive animation01 · Story
What to verify in this scene
Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.
- 01
Boundaries of linear inequalities become lines enclosing a feasible region
- 02
A linear objective selects the most favorable vertex of that region
- 03
The active constraints meet at optimal vertex opt=(2,2)
Linear programming is the geometry of boundaries and vertices
02 · Notebook
The runnable notebook
This source creates the mathematical objects and controls the order of operations and animation. Read it here, then play the same scene yourself.
2d
zoom 1/2
coordinates on
x = 0 #X0
y = 0 #Y0
x + y = 4 #C1
2x + y = 6 #C2
// Boundaries of linear inequalities become lines enclosing a feasible region
focus C1 C2
checkpoint Constraints & vertices
focus -
X0 -
Y0 -
// A linear objective selects the most favorable vertex of that region
solution(C1, C2) #opt@
// The active constraints meet at optimal vertex {{opt}}=`(2,2)`\nLinear programming is the **geometry of boundaries and vertices**
focus opt03 · Unit 8
Lessons in this unit
Linear programming & game theory — Use constraint vertices and payoff matrices to explore optimization applications.