How make a graphic with only equations ?

In linear programming , a mathematical model is defined with a set of constraints, a polygon is the result of these constraints (equations)

can mathlab I always make a plot with points (x,y) but I not work with only the equations

[Joseph Cheng]

Can you give a simple example of what you are trying to accomplish?

Answer 1

[Joseph Cheng]

if you have MuPad Notebook (part of the symbolic toolbox?) you can use it like here http://www.mathworks.com/help/symbolic/mupad_ref/linopt-plot_data.html

or my example here:

%%Constraints
% maximise Z = 20x + 10y
% 10x +5y <=50
% 6x + 10y <=60
% 4x+12y<=48
% x,y>=0

 %below portion done in MuPad
  k := [{10*x +5*y <=50,  6*x + 10*y <=60, 4*x+12*y<=48},20*x+10*y,NonNegative]:
  g := linopt::plot_data(k, [x, y]):
  plot(g):

[Joseph Cheng]

I've been thinking about what if you don't have MuPad well this is what i've got so far.

    %%Constraints
    % maximise Z = 20x + 10y
    % 10x +5y <=50
    % 6x + 10y <=60
    % 4x+12y<=48
    % 10x+y>=10 % unlike above my @ functions couldn't handle the infinity slope
    % x+10y>=10 %
    % x,y>=0

    CV{1} = [0 10;5 0]; %constraintvertices 1
    CV{2} = [0 6;10 0]; %constraintvertices 2
    CV{3} = [0 4;12 0]; %constraintvertices 3
    CV{4} = [0 10;1 0];
    CV{5} = [0 1;10 0];

    figure;hold all
    for ind = 1:length(CV)
    h(ind) = plot(CV{ind}(:,1),CV{ind}(:,2));
    end
    set(h,'linewidth',2)

    axis([0 10 0 12])

    slope = @(line) (line(2,2) - line(1,2))/(line(2,1) - line(1,1));
    intercept = @(line,m) line(1,2) - m*line(1,1);
    point = 1;
    for ind = 1:length(CV)-1
        for jnd = ind+1:length(CV)
            m1 = slope(CV{ind});
            m2 = slope(CV{jnd});
            b1 = intercept(CV{ind},m1);
            b2 = intercept(CV{jnd},m2);
            xintersect(point) = (b2-b1)/(m1-m2);
            yintersect(point) = m1*xintersect(point) + b1;
            point = point+1;
        end
    end
    plot(xintersect,yintersect,'r*','markersize',20)

Now you have a list of the all the intersections. Next step is to find the overlapping feasible region and remove the intersections that do not define the feasible region.

*update*

     %left hand side coefficients, -1 for <= +1 for >=, then right hand side
     Const = [10 5 -1 50;6 10 -1 60;4 12 -1 48;10 1 1 10; 1 10 1 10];

     for ind = 1:length(Const)
        switch Const(ind,3)
            case -1
                Fease(ind,:) = round(Const(ind,1)*xintersect+Const(ind,2)*yintersect) <= Const(ind,4);
            case 1
                Fease(ind,:) = round(Const(ind,1)*xintersect+Const(ind,2)*yintersect) >= Const(ind,4);
        end
     end

 %valid corner if all constraints are met
     corners = find(sum(Fease)/length(Const)==1)
     plot(xintersect(corners),yintersect(corners),'bo','markersize',20)

i'll let you figure out how to fill in the poly and how to get rid of the minute error involved in x and y intersect points which causes the inequalities to fail. Ideally if we check each intersect to be valid for each constraint then we mark it good.