# WHY the VERTICES? Linear Programming: A Closer Look

- Author:
- Tim Brzezinski

**Teachers:**When learning how to solve linear programming problems, students are taught that after graphing a feasible region in the coordinate plane (caused by some physical constraints), the maximum and minimum values of any objective function written in the form

*a*and

*b*are constants) ALWAYS occurs at one of the vertices (corners) of such a feasible region.

**But can our students explain WHY?**

*How does this applet help explain why?*

## Drag the BLUE POINT around the FEASIBLE REGION as much as you'd like! (You can also move the vertices of the feasible region.)

A special THANK YOU to

**Elina Formina**, HS Mathematics Teacher (Long Island, NY). Engaging in dialogue with her was what initially inspired me to create this.## Quick (Silent) Demo

## TO EXPLORE IN AUGMENTED REALITY:

1) Open up GeoGebra 3D Calculator on your device.
2) Go to the MENU (upper left corner). Select OPEN/SEARCH.
In the text field that appears, type

**hbffx3vk**. 3) The sliders**e**and**f**control the coefficients of the equation of the objective function (plane). The**SlideMe**slider shows the dynamic action. You can move the vertices of the feasible region and the large point in side this feasible region anywhere you'd like. (Just be sure to keep the vertices of this feasible region on the xy-plane itself).