Linear Programming - A Problem in 3D

Author:
Mr Malkin
I've got this linear programming problem in 3 variables: Maximise:  Subject to: I've heard that there's a flashy algorithm that will help me, but for now, let's try drawing it. My 3D drawing is below. Play around with the 3D view first*. Try to identify which plane relates to which constraint, and where the feasible region is. Then click "show objective function". Move it (i.e. change ) using the slider. At what point is maximised? (Look for the moment at which it leaves the feasible region completely.) What are the values of and at this point? Alternatively... at what point is minimised? *(Sometimes it drags with a left click, sometimes with a right click... try both.)