DualSimp

.

%Dual Simplex

clc;

clear all;

close all;

Z=[-3 -5]; %Enter cost

A=[-1 -3;-1 -1]; %Enter coefficient matrix

b=[-3;-2]; %Enter rhs column vector

variables=["x1","x2","s1","s2","Sol"];

s=eye(size(A,1));

Z=[Z zeros(1,size(b,1)) 0];

A=[A s b];

BV=[];

for j=1:size(s,2)

for i=1:size(A,2)

if A(:,i)==s(:,j)

BV=[BV i];

end

end

end

fprintf("Basic Variables:\n");

disp(variables(BV));

run=true;

while run

ZjCj=Z(BV)*A-Z;

table=[ZjCj;A];

simplexTable=array2table(table);

simplexTable.Properties.VariableNames(1:size(simplexTable,2))=variables;

disp(simplexTable);

if any(A(:,end)<0)

fprintf("Infeasible BFS.\n");

[leavingVal,pivotRow]=min(A(:,end));

fprintf("Leaving Row=%d \n",pivotRow);

Row=A(pivotRow,1:end-1);

Zrow=ZjCj(:,1:end-1);

for i=1:size(Row,2)

if Row(i)<0

ratio(i)=abs(Zrow(i)./Row(i));

else

ratio(i)=inf;

end

end

[minRatio,pivotCol]=min(ratio);

BV(pivotRow)=pivotCol;

fprintf("New Basic Variables:\n");

disp(variables(BV));

pivotVal=A(pivotRow,pivotCol);

A(pivotRow,:)=A(pivotRow,:)./pivotVal;

for i=1:size(A,1)

if i~=pivotRow

A(i,:)=A(i,:)-A(i,pivotCol).*A(pivotRow,:);

end

ZjCj=ZjCj-ZjCj(pivotCol).*A(pivotRow,:);

end

else

run=false;

fprintf("Feasible BFS.\n");

end

end