3.11 MATLAB Solution of LP Problems 157
4 x 1 +x 2 +x 3 ≤ 6
xi≥ 0 ; i= 1 , 2 , 3
SOLUTION
Step 1Express the objective function in the formf (x)=fTx nd identify the vectorsa
xandf as
x=
x 1
x 2
x 3
and f=
− 1
− 2
− 1
Express the constraints in the formAx≤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 simplex
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('LargeScale', 'off', 'Simplex', 'on');
- [x,fval,exitflag,output] = linprog(f,A,b,Aeq,beq,lb,[],[],
optimset('Display','iter'))
This produces the solution or output as follows:
Optimization terminated.
x=
0
4
2
fval =
-10
exitflag =
1
output =
iterations:3
algorithm: 'medium scale: simplex'
