function tab = SSSSimplex(A,b,c)
    validate_input(A,b,c);
    tab = Simplex(A,b,c);
end
%By Somesh
function tab = Simplex(A,b,c)
[m,n] = size(A);
tab = zeros(m+1,n+m+1);
tab(1:m,1:n) = A;
tab(1:m,end) = b;
tab(end,1:n) = c;
keep_running = true;
while keep_running
    if any(tab(end,1:n)>0)%check if there is negative cost coeff.
         [~,J] = max(tab(end,1:n)); %yes, find the most +tive
         % now check if corresponding column is unbounded
         if all(tab(1:m,J)<=0)
           error('problem unbounded. All entries <= 0 in column %d',J);
         %do row operations to make all entries in the column 0
         %except pivot
         else
             pivot_row = 0;
             min_found = inf;
             for i = 1:m
                  if tab(i,J)>0
                      tmp = tab(i,end)/tab(i,J);
                      if tmp < min_found
                          min_found = tmp;
                          pivot_row = i;
                      end                                                                           
                  end
             end
             %normalize
             tab(pivot_row,:) = tab(pivot_row,:)/tab(pivot_row,J);
             %now make all entries in J column zero.
             for i=1:m+1
                  if i ~= pivot_row
                      tab(i,:)=tab(i,:)-sign(tab(i,J))*...
                                    abs(tab(i,J))*tab(pivot_row,:);
                  end
             end
         end
    else
         keep_running=false;
    end
end    
end

function validate_input(A,b,c)
if ~ismatrix(A)
    error('A must be matrix');
end
 
if ~isvector(b)
    error('b must be vector');
end
if ~isvector(c)
    error('c must be vector');
end
 
                                                                                              
                                                                                              
[m,n]=size(A);
if rank(A) <m
    error('Rank A must be equal to number of rows in A');
end
 
if length(b) ~= m
    error('b must have same size as number of rows of A');
end
if length(c) ~= n
    error('c must have same size as number of columns of A');
end
end