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*xm-b` 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
>		x2-7x4      <=0
>		x2-x3+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*x-b
-730.5500
0
0
0

```