Graphical Linear Programming for Three Variables

show planes

hide objective function plane

objective function value

200

This Demonstration shows the graphical solution to the linear programming problem: maximize

4x+3y+6z

subject to

3x+5y+9z≤500

,

4x+5z≤350

,

2y+3z≤150

,

x≥0

,

y≥0

,

z≥0

. (The half-planes corresponding to the constraints are colored light blue, orange, and purple, respectively.) The image is oriented so that the feasible region is in front of the planes. When the "show planes" checkbox is not checked, the feasible region appears as a translucent red solid. The bright green plane is the level plane generated by setting the objective function equal to the value indicated by the slider.