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MOOOSE21

May 7th, 2025

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C= [11, 13, 17, 14; 16, 18, 14, 10; 21, 24, 13, 10];
S= [8 5 9];
D= [8 7 5 4];
[m ,n]= size(C);
if(sum(S)==sum(D))
disp('Balanced');
else if(sum(S)<sum(D))
C(end+1,:)=zeros(1,n);
S(end+1)= sum(D)- sum(S);
s=sum(D);
else
C(:,end+1)=zeros(m,1);
D(end+1)= sum(S)- sum(D);
s=sum(C);
end
end
table =C;
table= [table , S(:)];
mD = [D, s];
table= [table ; mD];
var ={'D1','D2','D3', 'D4', 'Supply' };
disp(array2table(table, 'VariableNames', var));
X=C;
Ci=C;
while any(S~=0)|| any(D~=0)
mini = min(C(:));
[r, c]= find(C==mini);
y = min(S(r), D(c));
[alloc, ind]= max(y);
rr= r(ind);
cc= c(ind);
X(rr, cc)= alloc;
S(rr)= S(rr)- alloc;
D(cc)= D(cc)-alloc;
C(rr, cc)= inf;
end
table =X;
table= [table , S(:)];
mD = [D, s];
table= [table ; mD];
var ={'D1','D2','D3', 'D4', 'Supply' };
disp(array2table(table, 'VariableNames', var));
Cost = Ci.*X;
[m, n]= size(X);
if nnz(X)==m+n-1
disp('Non-degenerate initial BFS');
else
disp('degenerate initial BFS');
end
final = sum(Cost(:));
disp("Total Cost is ");
disp(final);
//
C = [-3 2 0 0];
A = [1 1 1 0; 2 -1 0 1];
b = [6; 9];
m=size(A,1);
n=size(A,2);
bv_index=n-m+1:n;
Y=[A,b];
xb=Y(:,end);
cb=C(bv_index);
zicj= cb*Y(:,1:n)-C;
z=cb*xb;
table=[zicj,z;Y];
disp(table)
while any(zicj<0)
[~,ev]=min(zicj);
if all(Y(:,ev)<=0)
disp("unbounded")
return;
end
ratio=inf(1,m);
for j=1:m
if (Y(j,ev)>0)
ratio(j)=xb(j)/Y(j,ev);
end
end
[~,lv]=min(ratio);
bv_index(lv)=ev;
pivot=Y(lv,ev);
Y(lv,:)=Y(lv,:)/pivot;
for i=1:m
if i~=lv
Y(i,:)=Y(i,:)-Y(i,ev)*Y(lv,:);
end
end
xb=Y(:,end);
cb=C(bv_index);
zicj=cb*Y(:,1:n)-C;
z=cb*xb
table=[zicj,z;Y];
disp(table)
end
\\
clc;
clear;
% Objective function (Maximize Z = -3x + 2y)
C = [-3 2 0 0 -1e5 -1e5]; % Add Big M penalties (negative for maximization)
% Constraints (converted for simplex):
% x + y - s1 + a1 = 6
% 2x - y - s2 + a2 = 9
A = [1 1 -1 0 1 0;
2 -1 0 -1 0 1];
b = [6; 9];
[m, n] = size(A);
% Initial basic variables (artificial variables are basic initially)
bv_index = [5 6];
% Form initial tableau
Y = [A b];
% Initial values
xb = Y(:, end);
cb = C(bv_index);
% Compute initial Zj - Cj
zicj = cb * Y(:, 1:n) - C;
z = cb * xb;
table = [zicj z; Y];
disp('Initial Tableau:');
disp(table);
% Simplex loop
while any(zicj < 0)
[~, ev] = min(zicj); % Entering variable
if all(Y(:, ev) <= 0)
disp("Unbounded solution");
return;
end
ratio = inf(m, 1);
for j = 1:m
if Y(j, ev) > 0
ratio(j) = xb(j) / Y(j, ev);
end
end
[~, lv] = min(ratio); % Leaving variable
bv_index(lv) = ev;
% Pivot operation
pivot = Y(lv, ev);
Y(lv, :) = Y(lv, :) / pivot;
for i = 1:m
if i ~= lv
Y(i, :) = Y(i, :) - Y(i, ev) * Y(lv, :);
end
end
% Update tableau
xb = Y(:, end);
cb = C(bv_index);
zicj = cb * Y(:, 1:n) - C;
z = cb * xb;
table = [zicj z; Y];
disp('Next Tableau:');
disp(table);
end
% Final Result (no sign change needed for maximization)
fprintf('\nOptimal value (Max Z): %.2f\n', z);
for i = 1:n
val = 0;
if any(bv_index == i)
row = find(bv_index == i);
val = Y(row, end);
end
fprintf('Variable x%d = %.2f\n', i, val);
end
//
C = [-2 -1 0 0 0];
A = [-3 -1 1 0 0;
-4 -3 0 1 0;
-1 -2 0 0 1];
b = [-3; -6; -3];
[m, n] = size(A);
bv_index = n - m + 1:n;
Y = [A b];
xb = Y(:, end);
cb = C(bv_index);
while true
zicj = cb * Y(:, 1:n) - C;
z = cb * xb;
table = [zicj, z; Y];
disp("initial table")
disp(table);
if all(xb >= 0)
disp('Feasible Solution')
basic_var = bv_index;
xb
disp('Optimal Solution')
z
break
else
[~, lv] = min(xb);
if all(Y(lv, 1:n) >= 0)
disp('No feasible Solution');
break;
else
ratio = inf(1, n);
for j = 1:n
if Y(lv, j) < 0
ratio(j) = abs(zicj(j) / Y(lv, j));
end
end
[~, ev] = min(ratio);
bv_index(lv) = ev;
pivot = Y(lv, ev);
Y(lv, :) = Y(lv, :) / pivot;
for i = 1:m
if i ~= lv
Y(i, :) = Y(i, :) - Y(i, ev) * Y(lv, :);
end
end
xb = Y(:, end);
cb = C(bv_index);
end
end
end
disp(table);
//
clear all;
clc;
f= @(x1, x2)x1^2 -x1*x2 + x2^2;
grad= @(x1, x2)[2*x1- x2, 2*x2- x1];
x0=[1 , 0.5];
tol= 10^-5;
l= 0.01;
t= 100;
i=0;
x1=[0, 0];
while norm(t)>tol
g= -1* grad(x0(1), x0(2));
x1= x0 + l*g;
t= x1-x0;
x0=x1;
i= i+1;
end
M= f(x0(1), x0(2));
disp('point is');
disp(x0);
disp("minimum value at optimal point is :");
fprintf('%0.6f',M);
disp('no. of iteration are ');
disp(i);
//

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