How do i plot the function as a mesh in the constraint area only?

Given is the following conditions:

Using linprog()

Maximize: f= 30*X1 + 10*X2;

subject to : 6*X1 + 3*X2 <= 40;

3*X1 - X2<=0 ;

X1 + 0.25*X2 <= 4;

X1>=0

X2>=0

Display the plot

-the function as a mesh in the constraint area only (using mesh())

below is my approach ...please correct me.

f = [-30 -10];
A=[6 3;3 -1;1 0.25];
b=[40 0 4];
lb = zeros(2,1);
ub = [];
Aeq = [];
beq = [];

tic
options = optimoptions('linprog','Algorithm','dual-simplex','Display','iter');
[sol,fval,exitflag,output] = linprog(f,A,b,Aeq,beq,lb,ub,options);

LP preprocessing removed 0 inequalities, 0 equalities,
0 variables, and added 0 non-zero elements.

 Iter      Time            Fval  Primal Infeas    Dual Infeas  
    0     0.037    0.000000e+00   0.000000e+00   1.335997e+01  
    2      0.06   -1.600000e+02   2.057442e+00   0.000000e+00  
    3      0.06   -1.466667e+02   0.000000e+00   0.000000e+00  

Optimal solution found.

toc

Elapsed time is 1.673879 seconds.

[X1 X2]=meshgrid(0:0.2:50,0:0.2:50);
cons1= 6*X1 + 3*X2 <= 40;
cons2= 3*X1 - X2<=0 ;
cons3= X1 + 0.25*X2 <= 4;

X1(~cons1)= NaN;
X1(~cons2)= NaN;
X1(~cons3)= NaN;

X2(~cons1)= NaN;
X2(~cons2)= NaN;
X2(~cons3)= NaN;

f= 30*X1 + 10*X2;
mesh(X1,X2,f);

Answer 1

[yanqi liu]

sir，which is the question？

clc; clear all; close all;

f = [-30 -10];
A=[6 3;3 -1;1 0.25];
b=[40 0 4];
lb = zeros(2,1);
ub = [];
Aeq = [];
beq = [];

tic
options = optimoptions('linprog','Algorithm','dual-simplex','Display','iter');
[sol,fval,exitflag,output] = linprog(f,A,b,Aeq,beq,lb,ub,options);

LP preprocessing removed 0 inequalities, 0 equalities,
0 variables, and added 0 non-zero elements.

 Iter      Time            Fval  Primal Infeas    Dual Infeas  
    0     0.098    0.000000e+00   0.000000e+00   1.335997e+01  
    2     0.136   -1.600000e+02   2.057442e+00   0.000000e+00  
    3     0.137   -1.466667e+02   0.000000e+00   0.000000e+00  

Optimal solution found.

toc

Elapsed time is 2.145769 seconds.

[X1, X2]=meshgrid(0:0.1:20,0:0.1:20);
cons1= 6*X1 + 3*X2 <= 40;
cons2= 3*X1 - X2<=0 ;
cons3= X1 + 0.25*X2 <= 4;

X1(~(cons1&cons2&cons1))= NaN;
X2(~(cons1&cons2&cons1))= NaN;

f= 30*X1 + 10*X2;
mesh(X1,X2,-f);
xlabel('X1')
ylabel('X2')
zlabel('f')
hold on;
plot3(sol(1),sol(2),fval,'ro','MarkerFaceColor', 'r');