Solve and plot system in x and y with varying constants e and t

hello,

i am having troubles solving the following problem:

solve and plot for x and y

x+y+e+t>=0

And

x*y-e*t>=0

where x and y are the two variables while e and t are two constants whose values has to vary in a range

i am trying to see the effect of e and t on the system represented by x and y.

basically i would like to obtain on the same graph different curves in x and y for a fixed number of combinations of e and t.

my code so far is:

n= 21;
x = linspace(-100, 100, n);
y = linspace(-100, 100, n);
[X, Y] = meshgrid(x, y);
a = 50;
b = 5;
e = linspace(-a, a, b);
t = linspace(-a, a, b);
Z = zeros(n, n);
for k = 1:b
    for s = 1:b 
        b = X + Y + e(k) + t(s);
        d = X.*Y - e(k).*t(s);
        for i= 1:n
            for j= 1:n
                if b(i,j) >= 0
                    Z(i,j) = d(i,j);
                else
                    Z(i,j) = -1;
                end
            end
            v = [0, 0];
            contour(X, Y, Z, v, 'LineWidth', 1.5)
            grid on
            hold on
        end
    end
end

Warning: Colon operands must be real scalars. This warning will become an error in a future release.

Warning: Colon operands must be real scalars. This warning will become an error in a future release.

Warning: Colon operands must be real scalars. This warning will become an error in a future release.

Warning: Colon operands must be real scalars. This warning will become an error in a future release.

could anybody please give me any suggestions on how to improve it, as the result so far is not what i expect.

thank you very much

Answer 1

[Torsten]

basically i would like to obtain on the same graph different curves in x and y for a fixed number of combinations of e and t.

Inequalities produce 2d-regions, not 1d-curves as feasible sets. That's why it is difficult or even impossible to find an understandable plot of more than one feasible region for different values of e and t in one graph.

[LUCA D'AMBROSIO]

i have been a little unclear with my question, sorry.

i want to plot the boundary of the region where both inequalities are satisfied as function of varying e and t. basically i would like to obtain a curve for a defined set of combinations of e and t. that's why i want to plot curves and not 2d regions. is that possible to achieve? what am i doing wrong with my code?

sorry about the misunderstanding, i should have been clearer with what was my objective

[Torsten]

E = [100;200];
T = [1;5];
xleft = -25;
xright = 25;
nx = 10000;
x = linspace(xleft,xright,nx);
hold on
for j = 1:numel(E)
  e = E(j);
  t = T(j);
  f1 = @(x) -(x+e+t);
  f2 = @(x) e*t./x;
  count1 = 0;
  count2 = 0;
  for i = 1:numel(x)
    if x(i) >= 0
      count1 = count1 + 1;
      x1(count1) = x(i);
      px1(count1) = max(f1(x(i)),f2(x(i)));
    else
      count2 = count2 + 1;
      if f1(x(i)) <= f2(x(i)) 
        x2(count2) = x(i);
        px21(count2) = f1(x(i));
        px22(count2) = f2(x(i));
      else
        x2(count2) = x(i);
        px21(count2) = NaN;
        px22(count2) = NaN;
      end
    end
  end
  plot(x1,px1,'b')
  plot(x2,px21,'r')
  plot(x2,px22,'r')
end
hold off
grid on
ylim([-200 100])

[LUCA D'AMBROSIO]

thank you.

i have a follow up: how could i plot the same curve but for different values of e and t on the same figure? i tried nesting loops but it didn't work. thanks fo the help

[Torsten]

Done (see above).

[LUCA D'AMBROSIO]

thank you very much

Answer 2

[Walter Roberson]

for k = 1:b
    for s = 1:b 
        b = X + Y + e(k) + t(s);

You redefine b, which was used as the limit of your for loops.