How can i minimize

min h

45<= x1 + u1 -u3 -u4 <= 45 + h100

40<= x2 + u2 -u3 +u4 <= 40 + h100

80<= x3 + u3 <= 80 + h100

u1,u2,u3,u4 >= 0

u1<= 170 ,u2<= 50 , u3<= 100, u4<= 70

[Torsten]

What does h100 mean ? How is it related to h ?

Best wishes

Torsten.

Answer 1

[Titus Edelhofer]

Hi Jeffrey,

there is probably some missing information. I guess it's clear that h>=0. Since there are no restrictions on x1, x2, x3, you might choose

u1 = 0; u2 = 0; u3 = 0; u4 = 0;

x1 = 45; x2 = 40; x3 = 80;

=>

h = 0;

is the optimal solution... ? Or am I missing something?

Titus

[Jeffrey Eiyike]

I am suppose to minimise h .

Answer 2

[Jeffrey Eiyike]

That's the question on the jpg

Answer 3

[Titus Edelhofer]

Hi Jeffrey,

I'm not sure I fully understand. If u1, u2, u3, u4 and x (=x1,x2,x3) are given, the computing lambda is trivial. There is still some information missing.

Titus

[Jeffrey Eiyike]

u1<= 170 ,u2<= 50 , u3<= 100, u4<= 70 and x1= 130 x2= 120 x3= 150

Answer 4

[Titus Edelhofer]

Hi Jeffrey,

if I'm not mistaken, this should work:

% let the vector of unknowns be [u1 u2 u3 u4 lambda], then we
% have the following inequalities:
% u1 -u3 -u4 -lambda*100 <= 45-x1
% -u1 +u3 +u4 <= -45+x1
% and likewise for the other two
% in matrix form A*x<=b we have:

A = [ ...
   1  0 -1 -1 -100;
   0  1 -1  1 -100;
   0  0  1  0 -100;
  -1  0  1  1    0;
   0 -1  1 -1    0;
   0  0 -1  0    0];

% where b is:    
b = [45-130; 40-120; 80-150; -45+130; -40+120; -80+150];

% now solve for the unknowns: we don't care about u1, u2, u3, u4 but lambda should be small:
uLambda = linprog([0;0;0;0;1], A, b, [], [], [0;0;0;0;0], [170;50;100;70;inf])
% extract lambda
lambda = uLambda(5);

Titus