How to plot this functions for linear programming

2013 1 22
1 个回答
7 次查看（30 天）

0 个投票

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!

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Walter Roberson
Walter Roberson 2013-1-22
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
Danijel 2013-1-22
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
Walter Roberson 2013-1-22
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
Danijel 2013-1-22
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)

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回答（1 个）

Matt J
Matt J 2013-1-22
编辑：Matt J 2013-1-22

0 个投票

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"

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Danijel
Danijel 2013-1-22
"BTW, your objective function is quadratic, so I'm not sure why you call this a "linear programming problem"" That's truth...
Danijel
Danijel 2013-1-22
I am not sure about this h(x,y). I will try. Thanks.
Danijel
Danijel 2013-1-22
I tried, but the plot is strange. It's not giving the qudratic function.
Anyone? Help please?
Matt J
Matt J 2013-1-22
Help with what? How can we find your bugs if you don't show your code?
Danijel
Danijel 2013-1-22
编辑：Danijel 2013-1-22
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
Matt J 2013-1-22
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
Danijel 2013-1-22
编辑：Danijel 2013-1-22
Thanks Matt J. That's great...
Also, if you know, can Matlab show the Lagrange solution in any way?
Matt J
Matt J 2013-1-24
What is "the Lagrange solution"?
Danijel
Danijel 2013-2-8
Sorry Matt J. I didn't see your answer. The Lagrange solution is x=112; y=560; z=280; λ=15
Matt J
Matt J 2013-2-8
You can use the TEXT command to add annotation to plots

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Danijel
2013-1-22

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