*  NLP written by GAMS Convert at 11/29/04 16:22:45
*  
*  Equation counts
*      Total        E        G        L        N        X        C
*         98       98        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        136      136        0        0        0        0        0        0
*  FX     12       12        0        0        0        0        0        0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        501      159      342        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
          ,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
          ,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
          ,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128
          ,x129,x130,x131,x132,x133,x134,x135,x136;

Positive Variables  x12,x31,x38,x40,x47,x49,x56;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98;


e1..  - x2*x31 - 8*x3 + 8*x4 =E= 0;

e2..  - x2*x32 - 8*x4 + 8*x5 =E= 0;

e3..  - x2*x33 - 8*x5 + 8*x6 =E= 0;

e4..  - x2*x34 - 8*x6 + 8*x7 =E= 0;

e5..  - x2*x35 - 8*x7 + 8*x8 =E= 0;

e6..  - x2*x36 - 8*x8 + 8*x9 =E= 0;

e7..  - x2*x37 - 8*x9 + 8*x10 =E= 0;

e8..  - x2*x38 - 8*x10 + 8*x11 =E= 0;

e9..  - x2*x40 - 8*x12 + 8*x13 =E= 0;

e10..  - x2*x41 - 8*x13 + 8*x14 =E= 0;

e11..  - x2*x42 - 8*x14 + 8*x15 =E= 0;

e12..  - x2*x43 - 8*x15 + 8*x16 =E= 0;

e13..  - x2*x44 - 8*x16 + 8*x17 =E= 0;

e14..  - x2*x45 - 8*x17 + 8*x18 =E= 0;

e15..  - x2*x46 - 8*x18 + 8*x19 =E= 0;

e16..  - x2*x47 - 8*x19 + 8*x20 =E= 0;

e17..  - x2*x49 - 8*x21 + 8*x22 =E= 0;

e18..  - x2*x50 - 8*x22 + 8*x23 =E= 0;

e19..  - x2*x51 - 8*x23 + 8*x24 =E= 0;

e20..  - x2*x52 - 8*x24 + 8*x25 =E= 0;

e21..  - x2*x53 - 8*x25 + 8*x26 =E= 0;

e22..  - x2*x54 - 8*x26 + 8*x27 =E= 0;

e23..  - x2*x55 - 8*x27 + 8*x28 =E= 0;

e24..  - x2*x56 - 8*x28 + 8*x29 =E= 0;

e25..  - x2*x58 - 8*x31 + 8*x32 =E= 0;

e26..  - x2*x59 - 8*x32 + 8*x33 =E= 0;

e27..  - x2*x60 - 8*x33 + 8*x34 =E= 0;

e28..  - x2*x61 - 8*x34 + 8*x35 =E= 0;

e29..  - x2*x62 - 8*x35 + 8*x36 =E= 0;

e30..  - x2*x63 - 8*x36 + 8*x37 =E= 0;

e31..  - x2*x64 - 8*x37 + 8*x38 =E= 0;

e32..  - x2*x66 - 8*x40 + 8*x41 =E= 0;

e33..  - x2*x67 - 8*x41 + 8*x42 =E= 0;

e34..  - x2*x68 - 8*x42 + 8*x43 =E= 0;

e35..  - x2*x69 - 8*x43 + 8*x44 =E= 0;

e36..  - x2*x70 - 8*x44 + 8*x45 =E= 0;

e37..  - x2*x71 - 8*x45 + 8*x46 =E= 0;

e38..  - x2*x72 - 8*x46 + 8*x47 =E= 0;

e39..  - x2*x74 - 8*x49 + 8*x50 =E= 0;

e40..  - x2*x75 - 8*x50 + 8*x51 =E= 0;

e41..  - x2*x76 - 8*x51 + 8*x52 =E= 0;

e42..  - x2*x77 - 8*x52 + 8*x53 =E= 0;

e43..  - x2*x78 - 8*x53 + 8*x54 =E= 0;

e44..  - x2*x79 - 8*x54 + 8*x55 =E= 0;

e45..  - x2*x80 - 8*x55 + 8*x56 =E= 0;

e46..  - x4 + x82 =E= 0;

e47..  - x5 + x83 =E= 0;

e48..  - x6 + x84 =E= 0;

e49..  - x7 + x85 =E= 0;

e50..  - x8 + x86 =E= 0;

e51..  - x9 + x87 =E= 0;

e52..  - x10 + x88 =E= 0;

e53..  - 40*sqr(x4) + x114 =E= 18.38;

e54..  - 40*sqr(x5) + x115 =E= 18.38;

e55..  - 40*sqr(x6) + x116 =E= 18.38;

e56..  - 40*sqr(x7) + x117 =E= 18.38;

e57..  - 40*sqr(x8) + x118 =E= 18.38;

e58..  - 40*sqr(x9) + x119 =E= 18.38;

e59..  - 40*sqr(x10) + x120 =E= 18.38;

e60..  - sqr(cos(x22))*x114 + x122 =E= 0.12;

e61..  - sqr(cos(x23))*x115 + x123 =E= 0.12;

e62..  - sqr(cos(x24))*x116 + x124 =E= 0.12;

e63..  - sqr(cos(x25))*x117 + x125 =E= 0.12;

e64..  - sqr(cos(x26))*x118 + x126 =E= 0.12;

e65..  - sqr(cos(x27))*x119 + x127 =E= 0.12;

e66..  - sqr(cos(x28))*x120 + x128 =E= 0.12;

e67..  - 40*sqr(x4) + x130 =E= 18.5;

e68..  - 40*sqr(x5) + x131 =E= 18.5;

e69..  - 40*sqr(x6) + x132 =E= 18.5;

e70..  - 40*sqr(x7) + x133 =E= 18.5;

e71..  - 40*sqr(x8) + x134 =E= 18.5;

e72..  - 40*sqr(x9) + x135 =E= 18.5;

e73..  - 40*sqr(x10) + x136 =E= 18.5;

e74..  - 40*(9.81*sin(x21) - (0.25*sqr(x39 + x40)*sqr(cos(x21)) + 0.25*sqr(x48
       + x49))*x81) - 40*x57 + x89 =E= 0;

e75..  - 40*(9.81*sin(x22) - (0.25*sqr(x40 + x41)*sqr(cos(x22)) + 0.25*sqr(x49
       + x50))*x82) - 40*x58 + x90 =E= 0;

e76..  - 40*(9.81*sin(x23) - (0.25*sqr(x41 + x42)*sqr(cos(x23)) + 0.25*sqr(x50
       + x51))*x83) - 40*x59 + x91 =E= 0;

e77..  - 40*(9.81*sin(x24) - (0.25*sqr(x42 + x43)*sqr(cos(x24)) + 0.25*sqr(x51
       + x52))*x84) - 40*x60 + x92 =E= 0;

e78..  - 40*(9.81*sin(x25) - (0.25*sqr(x43 + x44)*sqr(cos(x25)) + 0.25*sqr(x52
       + x53))*x85) - 40*x61 + x93 =E= 0;

e79..  - 40*(9.81*sin(x26) - (0.25*sqr(x44 + x45)*sqr(cos(x26)) + 0.25*sqr(x53
       + x54))*x86) - 40*x62 + x94 =E= 0;

e80..  - 40*(9.81*sin(x27) - (0.25*sqr(x45 + x46)*sqr(cos(x27)) + 0.25*sqr(x54
       + x55))*x87) - 40*x63 + x95 =E= 0;

e81..  - 40*(9.81*sin(x28) - (0.25*sqr(x46 + x47)*sqr(cos(x28)) + 0.25*sqr(x55
       + x56))*x88) - 40*x64 + x96 =E= 0;

e82..  - (x121*x65 - 0.5*sin(x21)*x113*cos(x21)*(x39 + x40)*(x48 + x49) + 20*
      sqr(cos(x21))*x81*(x30 + x31)*(x39 + x40)) + x97 =E= 0;

e83..  - (x122*x66 - 0.5*sin(x22)*x114*cos(x22)*(x40 + x41)*(x49 + x50) + 20*
      sqr(cos(x22))*x82*(x31 + x32)*(x40 + x41)) + x98 =E= 0;

e84..  - (x123*x67 - 0.5*sin(x23)*x115*cos(x23)*(x41 + x42)*(x50 + x51) + 20*
      sqr(cos(x23))*x83*(x32 + x33)*(x41 + x42)) + x99 =E= 0;

e85..  - (x124*x68 - 0.5*sin(x24)*x116*cos(x24)*(x42 + x43)*(x51 + x52) + 20*
      sqr(cos(x24))*x84*(x33 + x34)*(x42 + x43)) + x100 =E= 0;

e86..  - (x125*x69 - 0.5*sin(x25)*x117*cos(x25)*(x43 + x44)*(x52 + x53) + 20*
      sqr(cos(x25))*x85*(x34 + x35)*(x43 + x44)) + x101 =E= 0;

e87..  - (x126*x70 - 0.5*sin(x26)*x118*cos(x26)*(x44 + x45)*(x53 + x54) + 20*
      sqr(cos(x26))*x86*(x35 + x36)*(x44 + x45)) + x102 =E= 0;

e88..  - (x127*x71 - 0.5*sin(x27)*x119*cos(x27)*(x45 + x46)*(x54 + x55) + 20*
      sqr(cos(x27))*x87*(x36 + x37)*(x45 + x46)) + x103 =E= 0;

e89..  - (x128*x72 - 0.5*sin(x28)*x120*cos(x28)*(x46 + x47)*(x55 + x56) + 20*
      sqr(cos(x28))*x88*(x37 + x38)*(x46 + x47)) + x104 =E= 0;

e90..  - (x129*x73 + 0.25*sin(x21)*x113*cos(x21)*sqr(x39 + x40) + 20*x81*(x30
       + x31)*(x48 + x49) + 392.4*cos(x21)*x81) + x105 =E= 0;

e91..  - (x130*x74 + 0.25*sin(x22)*x114*cos(x22)*sqr(x40 + x41) + 20*x82*(x31
       + x32)*(x49 + x50) + 392.4*cos(x22)*x82) + x106 =E= 0;

e92..  - (x131*x75 + 0.25*sin(x23)*x115*cos(x23)*sqr(x41 + x42) + 20*x83*(x32
       + x33)*(x50 + x51) + 392.4*cos(x23)*x83) + x107 =E= 0;

e93..  - (x132*x76 + 0.25*sin(x24)*x116*cos(x24)*sqr(x42 + x43) + 20*x84*(x33
       + x34)*(x51 + x52) + 392.4*cos(x24)*x84) + x108 =E= 0;

e94..  - (x133*x77 + 0.25*sin(x25)*x117*cos(x25)*sqr(x43 + x44) + 20*x85*(x34
       + x35)*(x52 + x53) + 392.4*cos(x25)*x85) + x109 =E= 0;

e95..  - (x134*x78 + 0.25*sin(x26)*x118*cos(x26)*sqr(x44 + x45) + 20*x86*(x35
       + x36)*(x53 + x54) + 392.4*cos(x26)*x86) + x110 =E= 0;

e96..  - (x135*x79 + 0.25*sin(x27)*x119*cos(x27)*sqr(x45 + x46) + 20*x87*(x36
       + x37)*(x54 + x55) + 392.4*cos(x27)*x87) + x111 =E= 0;

e97..  - (x136*x80 + 0.25*sin(x28)*x120*cos(x28)*sqr(x46 + x47) + 20*x88*(x37
       + x38)*(x55 + x56) + 392.4*cos(x28)*x88) + x112 =E= 0;

e98..    objvar - x2 =E= 0;

* set non default bounds

x2.lo = 0.1; 
x3.fx = 0.675; 
x11.fx = 0.675; 
x12.fx = 0; 
x20.fx = 2.09439333333333; 
x21.fx = 0.7853975; 
x29.fx = 0.7853975; 
x31.fx = 0; 
x38.fx = 0; 
x40.fx = 0; 
x47.fx = 0; 
x49.fx = 0; 
x56.fx = 0; 
x89.lo = -5; x89.up = 5; 
x90.lo = -5; x90.up = 5; 
x91.lo = -5; x91.up = 5; 
x92.lo = -5; x92.up = 5; 
x93.lo = -5; x93.up = 5; 
x94.lo = -5; x94.up = 5; 
x95.lo = -5; x95.up = 5; 
x96.lo = -5; x96.up = 5; 
x97.lo = -300; x97.up = 300; 
x98.lo = -300; x98.up = 300; 
x99.lo = -300; x99.up = 300; 
x100.lo = -300; x100.up = 300; 
x101.lo = -300; x101.up = 300; 
x102.lo = -300; x102.up = 300; 
x103.lo = -300; x103.up = 300; 
x104.lo = -300; x104.up = 300; 
x105.lo = -300; x105.up = 300; 
x106.lo = -300; x106.up = 300; 
x107.lo = -300; x107.up = 300; 
x108.lo = -300; x108.up = 300; 
x109.lo = -300; x109.up = 300; 
x110.lo = -300; x110.up = 300; 
x111.lo = -300; x111.up = 300; 
x112.lo = -300; x112.up = 300; 

* set non default levels

x2.l = 10000; 
x4.l = 0.675; 
x5.l = 0.675; 
x6.l = 0.675; 
x7.l = 0.675; 
x8.l = 0.675; 
x9.l = 0.675; 
x10.l = 0.675; 
x13.l = 0.523598333333333; 
x14.l = 0.7853975; 
x15.l = 1.04719666666667; 
x16.l = 1.30899583333333; 
x17.l = 1.570795; 
x18.l = 1.83259416666667; 
x19.l = 2.09439333333333; 
x22.l = 0.7853975; 
x23.l = 0.7853975; 
x24.l = 0.7853975; 
x25.l = 0.7853975; 
x26.l = 0.7853975; 
x27.l = 0.7853975; 
x28.l = 0.7853975; 
x39.l = 0.000209439333333333; 
x41.l = 0.000209439333333333; 
x42.l = 0.000209439333333333; 
x43.l = 0.000209439333333333; 
x44.l = 0.000209439333333333; 
x45.l = 0.000209439333333333; 
x46.l = 0.000209439333333333; 
x64.l = -4.32E-7; 
x66.l = -6.50521303491303E-23; 
x68.l = 1.30104260698261E-22; 
x69.l = -1.30104260698261E-22; 
x72.l = -1.67551466666667E-6; 
x80.l = -5.026544E-7; 
x81.l = 0.675; 
x82.l = 0.675; 
x83.l = 0.675; 
x84.l = 0.675; 
x85.l = 0.675; 
x86.l = 0.675; 
x87.l = 0.675; 
x88.l = 0.675; 
x89.l = 5; 
x90.l = 5; 
x91.l = 5; 
x92.l = 5; 
x93.l = 5; 
x94.l = 5; 
x95.l = 5; 
x96.l = 5; 
x98.l = -1.1984244510609E-21; 
x100.l = 2.3968489021218E-21; 
x101.l = -2.3968489021218E-21; 
x104.l = -3.43939841388793E-5; 
x105.l = 187.291497582168; 
x106.l = 187.291498184295; 
x107.l = 187.291498184295; 
x108.l = 187.291498184295; 
x109.l = 187.291498184295; 
x110.l = 187.291498184295; 
x111.l = 187.291498184295; 
x112.l = 187.291496347292; 
x113.l = 36.605; 
x114.l = 36.605; 
x115.l = 36.605; 
x116.l = 36.605; 
x117.l = 36.605; 
x118.l = 36.605; 
x119.l = 36.605; 
x120.l = 36.605; 
x121.l = 18.4225242836636; 
x122.l = 18.4225242836636; 
x123.l = 18.4225242836636; 
x124.l = 18.4225242836636; 
x125.l = 18.4225242836636; 
x126.l = 18.4225242836636; 
x127.l = 18.4225242836636; 
x128.l = 18.4225242836636; 
x129.l = 36.725; 
x130.l = 36.725; 
x131.l = 36.725; 
x132.l = 36.725; 
x133.l = 36.725; 
x134.l = 36.725; 
x135.l = 36.725; 
x136.l = 36.725; 

* set non default marginals


Model m / all /;

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

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

Solve m using NLP minimizing objvar;