simplex.m

clc
clear all
format short
NoofVariable=2;
c=[2 5];
a=[1 4;3 1;1 1]
b=[24;21;9]
s=eye(size(a,1))
A=[a s b]
cost=zeros(1,size(A,2))
cost(1:NoofVariable)=c
bv=NoofVariable+1:1:size(A,2)-1
zjcj=cost(bv)*A-cost
zcj=[zjcj;A]
simptable=array2table(zcj)
simptable.Properties.VariableNames(1:size(zcj,2))={'x1','x2','s1','s2','s3','sol'};
RUN=true;
while RUN
    if any(zjcj<0)
        fprintf('the current BFS is not optimal\n')
        zc=zjcj(1:end-1);
        [enter_val,pvt_col]=min(zc);
        if all(A(:,pvt_col)<=0)
            error('LPP is unbounded all enteries are <=0 in column %d',pvt_col);
        else
            sol=A(:,end);
            column=A(:,pvt_col);
            for i=1:size(A,1)
                if column(i)>0
                    ratio(i)=sol(i)./column(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:size(A,1)
            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(1:size(zcj,2))={'x1','x2','s1','s2','s3','sol'}
    else
        RUN=false;
        fprintf('The current BFS is optimal %f\n', zjcj(end))
    end
end