* System of nonlinear equations
* Steady state CSTRs with recycle (Kubicek et al., 1980)
* Different values of R can be used 

* Parameters
SCALAR D   / 22 /;

SCALAR beta1   / 2 /;

SCALAR beta2   / 2 /;

SCALAR R   / 0.935 /;

SCALAR gamma   / 1000 /;

VARIABLES
	 phi1  
	 phi2  
	 s  
     objval    objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 f Objective function
	 g1p  
	 g1m  
	 g2p  
	 g2m ; 

f  .. objval =e=s;
g1p  .. -phi1 - s + (1 - R)*(D/(10*(1+beta1))-phi1)*EXP(10*phi1/(1+10/gamma*phi1)) =l= 0;
g1m  .. phi1 - s - (1 - R)*(D /(10*(1+beta1))-phi1)*EXP(10*phi1/(1+10/gamma*phi1)) =l= 0;
g2p  .. phi1 - (1+beta2)*phi2 - s + (1 - R)*(D/10-beta1*phi1-(1+beta2)*phi2)*EXP(10*phi2/(1+10/gamma*phi2)) =l= 0;
g2m  .. -phi1 + (1+beta2)*phi2 - s - (1 - R)*(D/10-beta1*phi1-(1+beta2)*phi2)*EXP(10*phi2/(1+10/gamma*phi2)) =l= 0;

* Bounds
phi1.LO = 0;
phi1.UP = 1;
phi2.LO = 0;
phi2.UP = 1;

*Starting point (for R = 0.935)
* phi1.L = 0.724987;
* phi2.L = 0.245241;

MODEL test /ALL/;
SOLVE test USING NLP MINIMIZING objval;