Code to get matlab to solve for x and plug that number to the 2nd equation to find intersection point

Hello,

What a beautiful piece of software!.. thank you for making it! I'm trying to get some linear programming work done. and i'm having problems with finding the intersection of two equations on a plot. I have these two constraints

%      X + 2Y <= 16 #Constraint 1
%      5X+ 3Y <= 45 #Constraint 2
%      X, Y >= 0

My try was:

      clc, clear, close all

      % X + 2*Y <= 16
      x = [0 16];
      y = [8 0];

      % 5*X2 + 3*Y2 <= 45
      x2=[0 9];
      y2=[15 0];

      %%PLOTTING

      figure; plot(x,y, 'r');
      hold on 
      plot(x2,y2, 'b'); 
      hold off;
      title('Représentation Graphique du PL'), xlabel('x - Axe des abscisses'), ylabel('Y - Axe des Ordonnées');
      legend('X+2Y<=16', '5X+3Y<=45');

TRIED THIS CODE TO SHOW THE INTERSECTION POINT, BUT DIDN'T WORK...

%method 2
%---------
% sub = find(x == y)
% 
% x_intersect = y(sub);
% intersect_pt = y(sub);
% 
% figure(1);
% p = plot(x,y,...
%          x2,y2,...
%          x_intersect, intersect_pt, 'ko');

Thanks!

Answer 1

[Matías Nomboly]

In order to do this, I can show you a way to solve it, but its different from your approach I hope that what you are trying to find is the intersection between two functions, right?

So lets define a symbolic variable: syms x y 2) lets define both of the functions that you need as if they were equal to zero f1=x + 2*y - 16; f2=5*x + 3*y - 45;

3) we shall now solve for x or y in the second equation we'll choose to solve for y, just because I chose to yaux=solve(f2,'y');

4) we'll replace yaux in the f1 function f1x=subs(f1,'y',yaux);

5) Now f1x is only a function of x, so xintersection=solve(f1x); yintersection=subs(f1x,'x',xintersection);

so point (x,y) of intersection is (xintersection,yintersection) if you need them as a number you should do xintersection=double(xintersection); same for y intersection

code:

syms x y 
f1=x + 2*y - 16;
f2=5*x + 3*y - 45;
yaux=solve(f2,'y');
f1x=subs(f1,'y',yaux);
xintersection=solve(f1x);
yintersection=subs(f1x,'x',xintersection);
xintersection=double(xintersection); %if needed
yintersection=double(yintersection); %if needed

[Abdou Jadou]

Thanks for the reply, is it optimal if I keep solving those equations (constraints) I have on paper and adding those values for matlab to draw the equation lines ?

is there anyway to just insert the equation and have matlab calculate the points and draw the plot?

[Matías Nomboly]

No, i don't think that it would be optimal to solve this equations by hand because they are too easy for MATLAB and your PC. It would be if what you are trying to solve is way too hard or has sqrts and logs and exponentials and so on, all combined.

Regarding your second question, no, i do not know a standard matlab function that draws your plot and calculates intersections. However, there is a very practical equation plotter to help you visualize.

1) Define a symbolic variable

syms x

2) Define a function

f1=3*exp(x); (exp is e^x, euler's number)

3)Plot automatically

ezplot(f1);

4) Alternatively

ezplot(f1,[XLimMinimum, XLimMaximum]);

[Abdou Jadou]

You've been helpful, thank you.