% a linear programming problem is defined by
% (1) a linear objective function
% (2) a matrix of constraints
x = 0:80;
y1 = max(75-x,0);
y2 = max((4000-110*x)/30,0);
y3 = max((15000-120*x)/210,0);
ytop = min([y1; y2; y3]);
area(x,ytop);
hold on;
[u v] = meshgrid(0:80, 0:80);
contour(u,v,143*u + 60*v);
% using the linprog command
f = [-143 -60];
A = [120 210; 110 30; 1 1; -1 0; 0 -1];
b = [15000; 4000; 75; 0; 0];
linprog(f,A,b)
Optimization terminated.

ans =

   21.8750
   53.1250

sol = ans;
profit = -f*sol

profit =

  6.3156e+003

A*sol

ans =

  1.0e+004 *

    1.3781
    0.4000
    0.0075
   -0.0022
   -0.0053

diary off