simplex
Minimization of a linear objective function of several variables subject
to linear and positivity constraints.
[xm, cxm]=simplex(a,b,c)
[xm, cxm]=simplex(a,b,c, ctype)
Inputs 
a 
A real matrix. 
b 
A real vector with the same number of elements as the number of rows in a . 
c 
A real vector with the same number of elements as the number of columns in a . 
ctype 
A vector of integer elements with values in the set (1,1,0) , with the same number of elements as the number of rows in a .

Outputs 
xm 
A vector that minimzes the objective function c'*x with respect to x subject to the constraints defined below.

cxm 
The estimated minimum, i.e. c'*xm . 
Description
The minimization is subject to the constrints that none of the elements of
xm
are less than zero, and that the elements of the vector p=a*xmb
satisy p[i]>=0
, p[i]=0
, or p[i]<=0
depending on whether ctype[i]=1
,
ctype[i]=0
, or ctype[i]=1
. If ctype
is
not specified, it is assumed to be a vector of ones, i.e. the constraint
a*xm>=b
is satisfied.
Example
>>/*
> Solve
> Maximize x1+x2+3x.5x4
>
> subject to
> x1+2x2 <=740
> x27x4 <=0
> x2x3+2x4 >=.5
> x1+x2+x3+x4 =9
> x1,x2,x3,x4>=0
>*/
>>c=[1 1 3,.5]'
>>a=[1 0 2 0 ; 0,2,0,7;0,1,1,2;1 1 1 1 ]
>>b=[ 740,0,.5,9]'
>>ctypes=[1,1,1,0]'
>>(x,fx)=simplex(a,b,c,ctypes)
>>fx
17.0250
>>x
0
3.3250
4.7250
0.9500
>>a*xb
730.5500
0
0
0