Solving linear system with constraints

You only need to focus on lines '12' and below. For reference, the above vectors are part of a math problem I wanted to see how to "automate."

I would like to assign '35' a variable that finds the maximum value such that the largest value of 'ans' is equal to 105. I am new to MatLab and require logic associated with each step if possible. Thank you in advance.

Answer 1

[Askic V]

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Regarding the question you asked, please have a look at this example:

rng('default')
v = randi(100, 1, 15)

v = 1×15

82 91 13 92 64 10 28 55 96 97 16 98 96 49 81

% returns max element in v and its index 
[m,ind] = max(v)

m = 98

ind = 12

Answer 2

[Torsten]

x0 = 2;
sol = fmincon(@obj,x0,[],[],[],[],[],[],@nonlcon)

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

sol = 35.0000

function value = obj(x)
  value = -x;
end

function [c, ceq] = nonlcon(x)
  B = [0 1500 0];
  BC = [0 1 0];
  D = [-200 0 500];
  E = [500 0 500];
  BD = (D-B)/norm(D-B);
  BE = (E-B)/norm(E-B);
  matrix = [BD ;BE ;BC].';
  matrix2 = [0; 0; x];
  ans = matrix\matrix2;
  c = max(ans) - 105;
  ceq = [];
end