Ax=b question

Consider the matrix equation, Ax=b. Suppose I want to manipulate one of the values of b by increasing it in multiples of 100 until the maximum value within the x matrix exceeds 50000. What sort of code would I write to determine the size of the manipulated b value and which value of x exceeds 50000?

Answer 1

[Matt J]

You could use intlinprog. Assuming WNLOG that the manipulated b value is b(1),

N=numel(b);

f=[-1,zeros(1,N)].';
Aeq=[+100*f(1:N),A];
beq=[0;b(2:N)];
lb=[0;inf(N,1)];
ub=[inf;50000*ones(N,1)];

solution = intlinprog(f,1,[],[],Aeq,beq,lb,ub);

b_manipulated=100*solution(1)+100;

x=A\[b_manipulated;b(2:N)];

find(x>50000)