// This solves Example 5 in 9.3 of the Lin algebra text by Lay.
// We use -p as the scilab looks for a min
//
// Example 5 is:
// Maximize 25x_1 + 33x_2 + 18x_3 subject to
// 2x_1 + 3x_2 + 4x_3 <= 60
// 3x_1 +  x_2 + 5x_3 <= 46
//  x_1 + 2x_2 +  x_3 <= 50
// and x_1, x_2, x_3 >= 0
 
-->p=[25; 33; 18]
 p  =
 
    25.  
    33.  
    18.  
 
-->b=[60;46;50]
 b  =
 
    60.  
    46.  
    50.  
 
-->c=[2 3 4; 3 1 5;1 2 1]
 c  =
 
    2.    3.    4.  
    3.    1.    5.  
    1.    2.    1.  
 
-->[x,lagr,f]=linpro(-p,c,b,[0,0,0]',[])
 f  =
 
  - 693.42857  
 lagr  =
 
    0.         
    0.         
  - 30.714286  
    10.571429  
    1.2857143  
    0.         
 x  =
 
    11.142857  
    12.571429  
    0.         
 
-->diary(0)