I've got this linear programming problem in 3 variables:[br][br]Maximise: [br][math]P=x+y+2z[/math][br]Subject to:[br][math]x,y,z\ge0[/math][br][math]5x+7y+7z\le35[/math][br][br]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.[br][br]Play around with the 3D view first*. Try to identify which plane relates to which constraint, and where the feasible region is.[br][br]Then click "show objective function". Move it (i.e. change [math]P[/math]) using the slider. At what point is [math]P[/math] maximised? (Look for the moment at which it leaves the feasible region completely.) What are the values of [math]x,y,z[/math] and [math]P[/math] at this point?[br][br]Alternatively... at what point is [math]P[/math] minimised?[br][br]*(Sometimes it drags with a left click, sometimes with a right click... try both.)[br]