%% 0

lb = [0 0];
ub = [inf inf];
[x, fval] = linprog(-f, A, b, [], [], lb, ub); % x1 = 11.8857, x2 = 10.0571, fval = 21.9429

%% 1 x1 >= 12

lb = [12 0];
ub = [inf inf];
[x, fval] = linprog(-f, A, b, [], [], lb, ub); % x1 = 12, x2 = 8, fval = 20

%% 2 (x1 <= 11 ^ x1 >= 0)

lb = [0 0];
ub = [11 inf];
[x, fval] = linprog(-f, A, b, [], [], lb, ub); % x1 = 11, x2 = 10.5, fval = 21.5

%% 3 (x1 <= 11 ^ x1 >= 0) U (x2 <= 10 ^ x2 >= 0)

lb = [0 0];
ub = [11 10];
[x, fval] = linprog(-f, A, b, [], [], lb, ub); % x1 = 11, x2 = 10, fval = 21

%% 4 (x1 <= 11 ^ x1 >= 0) U (x2 >= 11)

lb = [0 11];
ub = [11 inf];
[x, fval] = linprog(-f, A, b, [], [], lb, ub); % x1 = 10, x2 = 11, fval = 21