Engineering Optimization: Theory and Practice, Fourth Edition

236 Linear Programming II: Additional Topics and Extensions

Express the constraints in the formA x≤band identify the matrixAand the

vectorbas

A=





2 1− 1

2 −1 5

4 1 1



 and b=







2

6

6







Step 2Use the command for executing linear programming program using interior

point method as indicated below:

clc

clear all

f=[–1;–2;–1];

A=[2 1—1;

2—1 5;

4 1 1];

b=[2;6;6];

lb=zeros(3,1);

Aeq=[];

beq=[];

options = optimset('Display', 'iter');

[x,fval,exitflag,output] = linprog(f,A,b,Aeq,beq,lb,[],[],

options)

This produces the solution or ouput as follows:

Iter 0: 1.03e+003 7.97e+000 1.50e+003 4.00e+002

Iter 1: 4.11e+002 2.22e–016 2.78e+002 4.72e+001

Iter 2: 1.16e–013 1.90e–015 2.85e+000 2.33e–001

Iter 3: 1.78e–015 1.80e–015 3.96e–002 3.96e–003

Iter 4: 7.48e–014 1.02e–015 1.99e–006 1.99e–007

Iter 5: 2.51e–015 4.62e–015 1.99e–012 1.98e–013

Optimization terminated.

x =

0.0000

4.0000

2.0000

fval = -10.0000

exitflag = 1

output =

iterations: 5

algorithm: 'large-scale: interior point'

cgiterations: 0

message: 'Optimization terminated.'