Simplex

.

%Simplex

clc;

clear all;

close all;

C=[2 5];

A=[1,4;3,1;1,1];

b=[24;21;9];

[m,n]=size(A);

s=eye(m);% identity matrix it creates

A=[A s b];

cost=zeros(1,n+m+1);

cost(1:n)=C;

bv=n+1:1:n+m;

zjcj=cost(bv)*A-cost;

zcj=[zjcj;A];

simptable=array2table(zcj);

simptable.Properties.VariableNames(1:size(A,2))={'x1','x2','s1','s2','s3','b'};

flag=true;

ratio=[];

while flag

if any(zjcj<0)

fprintf('curr not optimal');

zc=zjcj(1:end-1);

[Enter_val,pvt_col]=min(zc);

if all(A(:,pvt_col)<=0)

error('lpp unbounded all entries <=0 in col %d',pvt_col);

else

sol=A(:,end);

col=A(:,pvt_col);

for i=1:m

if col(i)>0

ratio(i)=sol(i)./col(i);

else

ratio(i)=inf;

end

end

[leaving_val,pvt_row]=min(ratio);

end

bv(pvt_row)=pvt_col;

pvt_key=A(pvt_row,pvt_col);

A(pvt_row,:)=A(pvt_row,:)./pvt_key;

for i=1:m

if i~=pvt_row

A(i,:)=A(i,:)-A(i,pvt_col).*A(pvt_row,:);

end

end

zjcj=zjcj-zjcj(pvt_col).*A(pvt_row,:);

zcj=[zjcj;A];

table=array2table(zcj);

table.Properties.VariableNames={'x1','x2','s1','s2','s3','sol'};

display(table);

else

flag=false;

end

end

display(table);