[b]Teachers:[/b][br][br]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 [br][br][math]z=ax+by[/math] (where [i]a[/i] and [i]b[/i] are constants) [br][br]ALWAYS occurs at one of the vertices (corners) of such a feasible region. [br][color=#9900ff][b]But can our students explain WHY? [/b][br][br][/color][i]How does this applet help explain why?[/i]

A special THANK YOU to [b]Elina Formina[/b], HS Mathematics Teacher (Long Island, NY). [br][br]Engaging in dialogue with her was what initially inspired me to create this.[br]

1) Open up GeoGebra 3D Calculator on your device.[br][br]2) Go to the MENU (upper left corner). Select OPEN/SEARCH.[br] In the text field that appears, type [b]hbffx3vk[/b]. [br][br]3) The sliders [b]e[/b] and [b]f[/b] control the coefficients of the equation of the objective function (plane). [br] The [b]SlideMe [/b]slider shows the dynamic action. [br][br] You can move the vertices of the feasible region and the large point in side this feasible region anywhere [br] you'd like. (Just be sure to keep the vertices of this feasible region on the xy-plane itself).