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Purpose: To provide a GAMS formulation for the collection
of Gupta Problems

Reference: Branch and bound experiments in convex nonlinear
integer programming, Management Science, 1533-1546, 31, 1985.

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Variables  i1,i2,i3,i4,i5,x6,x7,x8,objvar;

Positive Variables x6;

Integer Variables i1,i2,i3,i4,i5;

Equations  e1,e2,e3,e4;


e1..  - (0.0056858*i2*i5 + 0.0006262*i1*i4 - 0.0022053*i3*i5) + x6
      =E= 85.334407;

e2..  - (0.0071317*i2*i5 + 0.0029955*i1*i2 + 0.0021813*sqr(i3)) + x7
      =E= 80.51249;

e3..  - (0.0047026*i3*i5 + 0.0012547*i1*i3 + 0.0019085*i3*i4) + x8
      =E= 9.300961;

e4..  - (5.3578547*sqr(i3) + 0.8356891*i1*i5 + 37.293239*i1) + objvar
      =E= -40792.141;

* set non default bounds

i1.up = 200; 
i2.up = 200; 
i3.up = 200; 
i4.up = 200; 
i5.up = 200; 
x6.up = 92; 
x7.lo = 90; x7.up = 110; 
x8.lo = 20; x8.up = 25; 

* set non default levels

i1.l = 100; 
i2.l = 100; 
i3.l = 100; 
i4.l = 100; 
i5.l = 100; 

* set non default marginals


Model m / all /;

m.limrow=0; m.limcol=0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

Solve m using MINLP minimizing objvar;