No feasible solution in optimisation in linprog

My code:

f= [89;82;82;29;76];
A1= [0 0 2 1 0
    2 11 0 0 1
    60 60 0 0 8
    2 2 0 0 50
    15 9 0 0 8 
    0 0 20 14 9 
    4 0 60 14 0];
A= [A1;-A1];
AEQ= [1 1 1 1 1];
b= [100;140;120;130;140;150;60; -10; -100;-12;-13;-80;-13;-45];
alpha = 19:0.1:22;
advertisement=zeros(length(alpha),1);
obj_values = [];
x_values = [];
for i = 1:length(alpha)
    current_limit = alpha(i);
    [x, obj, exitflag, output] = linprog(f, A, b, AEQ, current_limit, [],[]);
    advertisement(i) = current_limit;
    x_values = [x_values,x];
    if exitflag == 1
        obj_values = vertcat(obj_values, obj);
    else
        obj_values = vertcat(obj_values, NaN);
    end
end

Hello, I'm not too sure where went wrong but it does not seems to produce any feasible solutions with regards to the problem that I have coded and there are no errors with the code. Would love if anyone could provide any advices.

Answer 1

[Matt J]

Your problem is infeasible because of the input problem data you provided, not because of coding errors. In particular, in Market Group 3, it is clear that you must allocate less than 3 to TVL and TVP in order to stay below the Saturation Level of 120. However, if TVP abd TVL are <3, there is no way for Market Group 2 to reach its Minimum Exposures of 100.

[Matt J]

If the optimization variables x(i) represent monetary expenditures, I'm assuming there should be non-negativity bounds on them as well, unless there are somehow ways to make negative expenditures in this scenario,

[x, obj, exitflag, output] = linprog(f, A, b, AEQ, current_limit, zeros(size(f)),[]);

[Jackie]

Thank you for the clarification! I'll check back with my tutor to see how it goes with regards to your comment!

Answer 2

[Alan Stevens]

I don't know if this will fix your problem, but I think the first number in the second row of A1 should be 8 not 2.

[Jackie]

Hello, thank you for spotting my mistake! Unfortunately, there's still no feasible solutions.

Answer 3

[John D'Errico]

I posted a question recently to help explain some of the reasons when linprog fails. You should read my first answer, as it discusses infeasibility by linprog.

https://www.mathworks.com/matlabcentral/answers/1847898-linprog-failed-to-work-why-did-i-do-something-wrong?s_tid=srchtitle

[Jackie]

Thank you for this information!