Representing polygon at an angle in 3D space with 2D shaded region on its x-y plane? (1 Viewer)

[MineTurtle]

Hi,

I've been working on a Simplex problem and would like to include a 3D graphical check where I graph the objective function (z=9x+7y) along with constraints (e.g. 10a+5b<=5010a+5b<=50, etc.) like this graph or page 2 of this pdf (so that I can visually confirm the solution as the highest point of the graph (in the z-direction): However on the various graphing software I have used so far, I can graph the objective function but I have to somehow represent the constraints in either Cartesian (z=f(x,y)z=f(x,y)) or Parametric (x,y,z)=f(u,v)(x,y,z)=f(u,v) form and although I have attempted to learn how this works, every time I try to enter the constraints, they don't appear with the 3D graph. I also cannot limit the objective function with linear constraints to form a polygon. Here is my attempt at graphing both the objecive function (shown in purple) with constraints (transparent pink): http://imgur.com/FJLOmPA but I have graphed the linear constraints as planes when they're meant to be flat on the x-y plane.

Any help or insight on how to represent 2D functions on a 3D plane or recommended free software that allows me to do this would be much appreciated. Thanks!

-MineTurtle

 

[leehuan]

Re: Representing polygon at an angle in 3D space with 2D shaded region on its x-y pla

Pretty sure GeoGebra has a 3D coordinate system but I'm not sure if it can be used to consider inequalities though.

Maybe combine it with WolframAlpha?
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I think this should be in the extracurricular section. "Mathematics" specifically refers to the 2U syllabus which goes nowhere near this stuff.

 

[MineTurtle]

Re: Representing polygon at an angle in 3D space with 2D shaded region on its x-y pla

Thanks, I'll definitely give those a go! Also thanks for letting me know I reposted in in the extracurricular section, I thought "Mathematics" meant maths in general haha.

-MineTurtle

 

[braintic]

Re: Representing polygon at an angle in 3D space with 2D shaded region on its x-y pla

In Geogebra, you would still need to sketch all planes at the start.
But then you find the intersection of the constraint planes with your "objective" plane to form a series of intersecting lines on the plane.
Then hide (not delete) the constraint planes.
Then find all the intersections of the lines on your plane.
Then hide the lines.
Then join the points of intersection using the polygon tool. (Assuming you are looking for a closed polygon)

 

[MineTurtle]

Re: Representing polygon at an angle in 3D space with 2D shaded region on its x-y pla

Thank you so much braintic! I just realised that I already have calculated the vertexes of where the objective function intersects with the constraints as a part of my solution and did what you said and it worked perfectly! I ended up with this (just need to make it look nicer).


-MineTurtle