Maximize z in the following linear program:

I have a question about Linear program

Given A = [1 1; -1 1; 0 -1], b = [10;10;0]

maximize z

subject to A(i) * x + z ≤ b(i) ∀i ∈{2,3}

-A(t) * x + z ≤ -b(t) ∀t ∈{1}

z ≤ 1 \\* or any other constant

[Dyuman Joshi]

Look into linprog.

What have you tried yet?

[Afuaab Koohg]

I have but the problem is unbounded:

x =[]

[Afuaab Koohg]

Here is my code

A = [1 1; -1 1; 0 -1]; b = [10;10;0];

f = zeros(size(A, 2) + 1, 1); % +1 for the z variable

i = [2,3]; t = [1]

% Define the inequality constraints for cplus and cminus

A_ineq = [A(i, :); -A(t, :)];

b_ineq = [b(i); -b(t)];

% Define the upper bounds for variables (no upper bound for x, z <= 1)

lb = -Inf(size(f));

ub = ones(size(f));

ub(end) = 1; % z <= 1

% Solve the linear program using linprog

options = optimset('Display', 'off'); % Suppress solver output

[x_z, ~, exitflag] = linprog(f, [], [], A_ineq, b_ineq, lb, ub, options);

[Matt J]

The problem formulaton does not do anything with the matrix A. Additionally, there is a vector a that has not been defined.

[Afuaab Koohg]

@Matt J: I have edited the question. It was a typo. I intended for A

[Torsten]

I get

x = [10 1]
z = 1

as solution.

A = [1 1; -1 1; 0 -1];  b = [10;10;0];
f = [0 0 -1];
i = [2,3]; t = [1];
% Define the inequality constraints for cplus and cminus
A_ineq = [A(i, :) ones(2,1); -A(t, :) ones(1,1)];
b_ineq = [b(i); -b(t)];
% Define the upper bounds for variables (no upper bound for x, z <= 1)
lb = -Inf(size(f));
ub = Inf(size(f));
ub(end) = 1; % z <= 1
% Solve the linear program using linprog
options = optimset('Display', 'off'); % Suppress solver output
[x_z, ~, exitflag] = linprog(f, A_ineq, b_ineq, [],[],lb, ub, options)

x_z = 3×1

10 1 1

exitflag = 1

[Afuaab Koohg]

@Torsten: Could you share your code becauise I get

[Torsten]

Done.