How to plot this functions for linear programming

I have this functions, and I want to plot them on same page because this is a problem in linear programing and I want to show both on same graph.

First is: f = x+0.0625*x^2 + y+0.0125*y^2 + z+0.025*z^2 (this is objective function)

Second is: g=x+y+z-952 (this is boundary)

Thanks!

[Walter Roberson]

Is one of the variables, x or y or z, being held as a constant? If not then you would be trying to plot in 4 dimensions, (x, y, z, f) which is going to be a problem.

[Danijel]

Since I solved the problem with Lagrange method, I have the values for x,y,z, and λ - Lambda (the Lagrange multiplier). Maybe this could be useful... The solved values are: x=112; y=560; z=280; λ=15

[Walter Roberson]

Are you asking to plot a single point, f(112,560,280) ??

If you are wanting to plot f over a range of values of x, and a range of values for y, and a range of values for z, then you need x, y, and z graphic axes to represent the inputs, but you also need another graphics axis to represent the result f(x,y,z) -- a 4 dimensional plot. Is that what you were thinking of?

[Danijel]

The second approach would be something what I was thinking of. I tried to plot the first function with isosurface, but I'm not sure wether this is truth what I'm getting as a result, because as I don't know which value for isovalue to set? Also, I don't know how to plot the g function on the same page...

[x,y,z] = meshgrid( linspace( -120, 600, 300 ) ); f = x+0.0625*x.^2 + y+0.0125*y.^2 + z+0.025*z.^2; isosurface(x, y, z, f, 476)

Answer 1

[Matt J]

Since the solution has to satisfy

 x+y+z=952

why not eliminate one of the variables, e.g.

 h(x,y) = f(x,y,952-x-y)

and plot the 2D surface h(x,y) only? Why care about any other region?

BTW, your objective function is quadratic, so I'm not sure why you call this a "linear programming problem"

[Danijel]

"BTW, your objective function is quadratic, so I'm not sure why you call this a "linear programming problem"" That's truth...

[Danijel]

I am not sure about this h(x,y). I will try. Thanks.

[Danijel]

I tried, but the plot is strange. It's not giving the qudratic function.

Anyone? Help please?

[Matt J]

Help with what? How can we find your bugs if you don't show your code?

[Danijel]

This is the solution and the plot of the function I tried to plot:

syms x y z Lambda f=x+0.0625*x^2+y+0.0125*y^2+z+0.025*z^2 g=x+y+z-952 L=jacobian(f,[x y z])-Lambda*jacobian(g,[x y z]) [Lambdasoln,xsoln,ysoln,zsoln]=solve(L,g) [x,y,z] = meshgrid( linspace( -120, 600, 300 ) ); f = x+0.0625*x.^2 + y+0.0125*y.^2 + z+0.025*z.^2; isosurface(x, y, z, f, 476)

I tried with the 2D plot also but it gives the surface, and since it is quadratic, something's wrong...

[Matt J]

How about

[x,y] = meshgrid( linspace( -120, 600, 300 ) ); 

f =@(x,y,z) x+0.0625*x.^2 + y+0.0125*y.^2 + z+0.025*z.^2; 
h= f(x,y,952-x-y);

surf(x,y,h)

[Danijel]

Thanks Matt J. That's great...

Also, if you know, can Matlab show the Lagrange solution in any way?

[Matt J]

What is "the Lagrange solution"?

[Danijel]

Sorry Matt J. I didn't see your answer. The Lagrange solution is x=112; y=560; z=280; λ=15

[Matt J]

You can use the TEXT command to add annotation to plots