function opt
m = 15;
x = 0:m;
y1 = 4-x;
y2 = (12-x)/3;
y3 = (0-x)/-1;
ybottom = max([y1; y2; zeros(1,size(x,2))]);
ytop = max([y3; zeros(1,size(x,2))]);
area(x,ytop);
hold on;
area(x,ybottom);
[u  v] = meshgrid(0:m,0:m);
contour(u,v,2*u+v);
hold off;
f = [2  1]
A = [-1 -3; -1 -1; -1 1; -1 0; 0 -1]
b = [-12; -4; 0; 0; 0]
linprog(f,A,b)
f*ans