// problem M2 

// 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,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30;

EQUATIONS e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19,e20,e21;

e1: -6*x1+x2-9*x3+3*x5+x6+4*x7-2*x8+8*x9-6*x10-4*x11-6*x13+3*x14+6*x15+2*x16+x17+9*x18+8*x19-10*x20-4*x21-7*x22-8*x23-x24+5*x25-7*x26+10*x27-3*x28-6*x29-7*x30 <= -5;

e2: -9*x1-8*x2+3*x3-5*x4+5*x5+6*x6+9*x7-7*x8-x9+4*x10+x11+3*x12+10*x13-6*x14-7*x15-5*x16-4*x17-x18-5*x19+6*x21-4*x22+9*x23-5*x24+9*x25+5*x26-x27+4*x28+6*x29+6*x30 <= 37;

e3: 4*x1+3*x2+8*x3-8*x4+5*x5-9*x6-5*x7+x8-7*x9+8*x10+4*x12-7*x13-6*x14-2*x15-4*x16+2*x17+9*x18+9*x19-8*x20-3*x21+7*x22-6*x23+3*x24-5*x25-7*x26-3*x27+2*x28+x29+9*x30 <= 12;

e4: 4*x1-2*x2-5*x3+9*x4+10*x5+x6-6*x7-5*x8+9*x9-5*x10-8*x11-6*x12+3*x13-8*x14+2*x15+4*x16-4*x18-5*x19-7*x20+4*x21+4*x22-3*x23-8*x24-3*x25-9*x26-x27+7*x28+3*x29-7*x30 <= -11;

e5: 9*x1+4*x2-x3-9*x4+8*x5-4*x7-2*x9+7*x10-2*x11+8*x12+2*x13-2*x14-6*x15-8*x16-x17-x18+7*x19+8*x20-4*x21+2*x22+2*x23-6*x24+5*x25+3*x26+5*x27+5*x28+7*x29+2*x30 <= 59;

e6: -2*x1+8*x2+5*x3-5*x5+9*x6+8*x7-x8-7*x9-x10+2*x11+7*x12-10*x13+9*x14+7*x15+5*x16-5*x17+4*x19+6*x20-10*x21+4*x22+2*x23-8*x24-8*x26-6*x27+7*x28-5*x29-9*x30 <= 26;

e7: 5*x2-2*x4-4*x5+5*x6+3*x7+9*x8+8*x9+8*x11+8*x12-10*x13+9*x14-7*x15+x16-3*x17+3*x18-x19+5*x20-8*x21-3*x22-7*x23+x24+5*x25+9*x26-7*x27+4*x28+4*x29-3*x30 <= 51;

e8: 7*x1-5*x2-5*x3-4*x4-3*x5+x6-7*x7-7*x8-8*x9+2*x10-x11+x12+5*x13-2*x14+10*x15+x16-2*x17-2*x18+6*x19-x20-9*x22+x23-10*x24+3*x25-3*x27-2*x28-5*x29-4*x30 <= -24;

e9: -9*x1-9*x2-5*x3+8*x4+x6+4*x7-6*x8-7*x9+6*x10+5*x11-7*x12+5*x13-5*x14-5*x15+2*x16-x17+2*x18-10*x19-10*x20+6*x21+10*x22+9*x23-6*x24+4*x25+2*x26+9*x27+9*x28-2*x29 <= 25;

e10: -9*x1+5*x2-3*x3+x4+2*x5+2*x6-2*x7-4*x8-9*x9+5*x10+7*x11-x12-4*x13+4*x14-5*x15-3*x16+10*x18-7*x19+2*x20-6*x21+x22-3*x23+2*x24+5*x25+8*x26+9*x27+2*x28-8*x29+7*x30 <= 27;

e11: x1-3*x2-7*x3-x4+7*x5+7*x6-2*x7+3*x8-3*x9-x10+4*x11+10*x12-2*x13-4*x14-8*x15+4*x16-2*x17-7*x18+4*x19-9*x21-10*x22+7*x23-x24-9*x25-10*x26-5*x27-3*x28-x29+7*x30 <= -15;

e12: 3*x1+3*x2+9*x4-2*x5-7*x6-7*x8-5*x9+9*x10+6*x11-6*x12+4*x13+6*x14-6*x15-7*x16-4*x17+3*x18+4*x19-9*x20-9*x21+7*x22+9*x23-8*x24-5*x25+2*x26-9*x27+x28-5*x29+5*x30 <= 1;

e13: -10*x1+5*x2+8*x3-9*x4+7*x5-6*x6-7*x7+3*x8-7*x9+3*x10+4*x11-x12+4*x13+6*x14+3*x15-7*x16-8*x17-3*x18-x19+x20-7*x21-9*x22-5*x23+4*x24-6*x25+4*x26-8*x27-x28+6*x29-3*x30 <= -22;

e14: -2*x1+10*x2+8*x3+5*x4-5*x5+4*x6+2*x7+2*x8+6*x9-x10+5*x11-4*x12-6*x13-2*x14+4*x15-3*x17+x18+2*x19-2*x20+4*x21-2*x22-5*x23-2*x24+x25+x27-2*x28+6*x30 <= 44;

e15: -9*x1-3*x2-9*x3+5*x4-2*x5-7*x6+7*x7+6*x8-x9+6*x10-10*x11+7*x13-4*x14+6*x15+7*x16-5*x17+5*x19-6*x20-4*x21-2*x23+7*x24+3*x25-9*x26-7*x27-5*x28-10*x29+3*x30 <= -9;

e16: -2*x1-5*x2+8*x3+7*x4+x5-8*x6+2*x7-5*x8-3*x9+4*x10+8*x11+8*x12+4*x13-6*x14+4*x15+6*x16+3*x17+7*x18+10*x19-2*x20-9*x21+2*x22+6*x23-8*x24+2*x25-x26-8*x28-5*x29-9*x30 <= 29;

e17: 4*x1+10*x2-7*x4-x5-5*x6+9*x7-x9+4*x10-x12+7*x13-10*x14+5*x15+x16+4*x17-10*x18+4*x19+3*x20+5*x22+8*x23+9*x24-3*x25-8*x27-2*x28+3*x29-9*x30 <= 39;

e18: 2*x1+4*x2-10*x4-4*x5-10*x6+x7-2*x8+6*x9+10*x10-x11-x12-8*x13-6*x14+3*x15+5*x16-5*x18-4*x19+3*x20-x21+4*x22-5*x23-9*x24-6*x25+5*x26+7*x27-x28-x29-7*x30 <= -10;

e19: 9*x1+5*x2-4*x3+4*x4-6*x5-2*x6-7*x7-6*x8+9*x9+9*x10-9*x11+6*x12-8*x13+10*x14+3*x15-4*x16+5*x17+3*x18+5*x19+4*x20+x22+5*x23-8*x24-5*x25-9*x26-3*x27-4*x28-6*x29+5*x30 <= 20;

e20: 5*x1+9*x2+2*x3+2*x4+x5+7*x6+7*x7+5*x8+3*x9+7*x10+4*x11+2*x12+2*x13+4*x14+5*x15+9*x16+10*x17+5*x18+x19+5*x20+x21+8*x22+6*x23+8*x24+3*x25+2*x26+5*x27+4*x28+4*x29+10*x30 <= 1680;

e21: 0.204037*x1+0.204037*x2-0.116593*x3-0.204037*x4+0.291482*x5+0.0874446*x6-0.0291482*x7+0.262334*x8+0.116593*x9+0.174889*x10+0.0291482*x11+0.0291482*x12-0.204037*x13+0.262334*x14+0.174889*x15-0.204037*x16-0.262334*x17-0.0874446*x18-0.233186*x19-0.233186*x20+0*x21-0.291482*x22+0.0291482*x23+0.204037*x24+0.0874446*x26+0.145741*x27+0.116593*x28-0.291482*x29-0.174889*x30 <= -36.2288;


OBJ: minimize 14571.3*x1-37250.2*x2+1578.41*x3-23199.3*x4-36532.1*x5+14992*x6-46241.9*x7+59634*x8+11781.2*x9-62617.5*x10+23226.7*x11-16497.4*x12+350.559*x13+25674.8*x14+56334.3*x15-2159.25*x16+30151*x17-13688.3*x18-41755.3*x19+34911.7*x20+104801*x21-47888.5*x22-10644.3*x23+119299*x24+27859.5*x25+89793.8*x26+108734*x27-31798.4*x28+15961.7*x29-5450.71*x30-3*x1^2-x2^2-7*x3^2-7*x4^2-9*x5^2-4*x6^2-6*x7^2-8*x8^2-x9^2-x10^2-6*x11^2-7*x12^2-x13^2-4*x14^2-2*x15^2-5*x16^2-7*x17^2-6*x18^2-9*x19^2-9*x20^2-6*x21^2-2*x22^2-7*x23^2-5*x24^2-7*x25^2-9*x26^2-8*x27^2-3*x28^2-x29^2-8*x30^2;