% 9.1 an optimization problem
% p(x,y) = 143*x + 60*y  
% 110*x + 30*y <= 4000
% 120*x + 210*y <= 15000
% x + y <= 75
x = 0:80;  % range for x
y1 = max((4000-110*x)/30,0);
y2 = max((15000 - 120*x)/210,0);
y3 = max(75-x,0);
ytop = min([y1,y2,y3]);  % upper values that are allowed for y
area(x,ytop)
ytop = min([y1;y2;y3]);  % upper values that are allowed for y
area(x,ytop)
hold on
[u  v]=meshgrid(0:80,0:80);
contour(u,v,143*u + 60*v);
% linprog 
%    min f*x  subject to A*x <= b
f = [-143  -60]  % flip signs because we want to maximize

f =

  -143   -60

A = [110  30
           120 210
             1    1
           -1  0
            0  -1]

A =

   110    30
   120   210
     1     1
    -1     0
     0    -1

b = [4000;   15000;  75;  0; 0]

b =

        4000
       15000
          75
           0
           0

sol = linprog(f,A,b)
Optimization terminated successfully.

sol =

   21.8750
   53.1250

profit = -f*sol

profit =

  6.3156e+003

format bank
profit

profit =

       6315.62

diary off