Solving a system of linear inequalities

Dear all, I need your help to solve a system of linear inequalities. The system is as follows

Fx = [x1+x2; x1+x2+x3+x6+x7; x2+x3+x4+x6; x3+x4+x5+x7; x4+x5; x2+x3+x6; x2+x4+x7]

and Fx >= 1

given that x1,x2,...x7 can either = 0 or 1 (whole number)

How to solve x1,x2 up to x7 in MATLAB?

Thanks in advance.

Best Regards

Cassandra

[Torsten]

Choose

x1 = x2 = x3 =...= x7 = 1

Then

Fx >= 1 (componentwise)

is satisfied.

Best wishes

Torsten.

Answer 1

[Bjorn Gustavsson]

...or if you want all points that satisfy the conditions you could do:

D = {[0 1],[0 1],[0 1],[0 1],[0 1],[0 1],[0 1]};
[X1,X2,X3,X4,X5,X6,X7] = ndgrid(D{:});
IOK = (X1+X2>=1 & X1+X2+X3+X6+X7>=1 & X2+X3+X4+X6>=1 & X3+X4+X5+X7>=1 & X4+X5>=1 & X2+X3+X6>=1& X2+X4+X7>=1);

HTH

[John D'Errico]

I repaired a typo for you.

[Bjorn Gustavsson]

Thanks. What did I goof on this time?

[John D'Errico]

The last [0 1] in your assignment of D was given as [01], with no space. So a pretty minor typo.

[Edward Szymkowiak]

I am having trouble decoding IOK. Here is a simpler version:

D = {[0 1 ],[0 1],[0 1 ] };

[X1,X2,X3] = ndgrid(D{:});

IOK = (X1+X2+X3>0 & -X1+X2-X3>0);

Every time I add another variable the dimension of IOK increases.

Is there some code to map IOK back into a readable form telling us what values of X(n) satisfy the system for n =1 to # of variables?

Thanks