// problem M1

// use the specialized module for Separable Concave Quadratic Programming

MODULE: SCQP;

POSITIVE_VARIABLES x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12,
x13, x14, x15, x16, x17, x18, x19, x20;

EQUATIONS e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11;

e1: -6*x1+ 1*x2+ 1*x3 -3*x4 -9*x5 -7*x6 -0*x7 -1*x8+ 3*x9+ 7*x10+ 1*x11+ 7*x12+ 4*x13 -2*x14 -2*x15+ 3*x16+ 8*x17 -3*x18 -6*x19 -1*x20 <= 5;

e2: -9*x1+ 3*x2 -8*x3+ 3*x4+ 3*x5 -0*x6 -5*x7+ 9*x8+ 5*x9 -2*x10+ 6*x11 -7*x12+ 9*x13 -0*x14 -7*x15 -7*x16 -1*x17 -5*x18+ 4*x19+ 9*x20 <= 8;

e3: 4*x1 -10*x2+ 3*x3+ 5*x4+ 8*x5+ 8*x6 -8*x7 -9*x8+ 5*x9+ 7*x10 -9*x11 -6*x12 -5*x13 -7*x14+ 1*x15+ 3*x16 -7*x17 -7*x18+ 8*x19+ 3*x20 <= -5;

e4: 4*x1 -2*x2 -2*x3+ 10*x4 -5*x5+ 8*x6+ 9*x7+ 5*x8+ 10*x9 -5*x10+ 1*x11+ 4*x12 -6*x13+ 2*x14 -5*x15+ 2*x16+ 9*x17+ 6*x18 -5*x19 -1*x20 <= 49;

e5: 9*x1 -9*x2+ 4*x3 -3*x4 -1*x5 -9*x6 -9*x7+ 5*x8+ 8*x9 -2*x10 -0*x11 -7*x12 -4*x13+ 7*x14 -0*x15+ 6*x16 -2*x17 -1*x18+ 7*x19+ 6*x20 <= 17;

e6: -2*x1 -2*x2+ 8*x3 -5*x4+ 5*x5+ 8*x6+ 0*x7+ 7*x8 -5*x9+ 1*x10+ 9*x11 -8*x12+ 8*x13+ 2*x14 -1*x15 -5*x16 -7*x17 -3*x18 -1*x19+ 4*x20 <= 22;

e7: 0*x1+ 4*x2+ 5*x3+ 10*x4 -0*x5+ 0*x6 -2*x7 -7*x8 -4*x9 -1*x10+ 5*x11 -5*x12+ 3*x13+ 9*x14+ 9*x15 -0*x16+ 8*x17 -1*x18+ 0*x19+ 4*x20 <= 46;

e8: 7*x1+ 2*x2 -5*x3+ 4*x4 -5*x5+ 0*x6 -4*x7 -10*x8 -3*x9 -4*x10+ 1*x11 -10*x12 -7*x13+ 1*x14 -7*x15 -2*x16 -8*x17+ 6*x18+ 2*x19+ 10*x20 <= -23;

e9: -9*x1+ 9*x2 -9*x3+ 5*x4 -5*x5 -4*x6+ 8*x7+ 4*x8+ 0*x9 -6*x10+ 8*x11 -2*x12+ 4*x13 -7*x14 -6*x15 -6*x16 -7*x17+ 9*x18+ 6*x19+ 9*x20 <= 11;

e10: 3*x1+ 5*x2+ 5*x3+ 1*x4+ 4*x5+ 6*x6+ 9*x7+ 5*x8+ 7*x9+ 9*x10+ 7*x11+ 8*x12+ 7*x13+ 7*x14+ 0*x15+ 9*x16+ 5*x17+ 5*x18+ 1*x19+ 7*x20 <= 1210;

e11: 1.236128465145494e-01*x1+ 1.648171286860659e-01*x2 -2.472256930290987e-01*x3+ 3.296342573721317e-01*x4+ 2.884299752006152e-01*x5+ 3.296342573721317e-01*x6+ 4.120428217151646e-02*x7 -2.884299752006152e-01*x8 -4.120428217151646e-02*x9+ 4.120428217151646e-01*x10 -2.472256930290987e-01*x11 -4.120428217151646e-02*x12 -1.648171286860659e-01*x13+ 0.000000000000000e+00*x14+ 3.296342573721317e-01*x15 -4.120428217151646e-02*x16 -4.120428217151646e-02*x17+ 2.472256930290987e-01*x18 -1.236128465145494e-01*x19 -2.472256930290987e-01*x20 <= -5.522163989931984e+00;


OBJ: minimize 5.407921297315957e+02*x1+ 9.200680036286360e+01*x2 -2.390752520391342e+03*x3 -8.085401304791822e+03*x4 -4.627101733281909e+03*x5 -1.245270983528748e+04*x6+ 9.419178740685280e+03*x7+ 7.689141305662554e+03*x8 -5.154768651245953e+03*x9 -9.814998603125452e+03*x10 -3.701153042020248e+03*x11+ 1.281844895334844e+04*x12 -7.825528467430385e+03*x13 -5.260531897817202e+01*x14+ 6.727681144133561e+03*x15+ 6.093302802991371e+03*x16 -1.139496583573926e+03*x17+ 7.666776687267717e+03*x18+ 7.371886470176738e+03*x19 -1.641291168073667e+04*x20 -3*x1^2-1*x2^2-7*x3^2-7*x4^2-9*x5^2-4*x6^2-6*x7^2-8*x8^2-1*x9^2-1*x10^2-6*x11^2-7*x12^2-1*x13^2-4*x14^2-2*x15^2-5*x16^2-7*x17^2-6*x18^2-9*x19^2-9*x20^2;