min: 3 x12 + 4 x13 +5 x14 +2 x15 +5 x23 + 6 x24 + 7 x25 +7 x34 +8 x35 +9 x45 + 3 x21 + 4 x31 +5 x41 +2 x51 +5 x32 + 6 x42 + 7 x52 +7 x43 +8 x53 +9 x54; x12 + x13 + x14+ x15 =1; x23 + x24 + x25 + x21 = 1; x31 + x32 + x34 + x35 = 1; x41 + x42 + x43 + x45 = 1; x51 + x52 + x53 + x54 =1; x21 + x31 + x41+ x51 =1; x32 + x42 + x52 + x12 = 1; x13 + x23 + x43 + x53 = 1; x14 + x24 + x34 + x54 = 1; x15 + x25 + x35 + x45 =1; binary x12, x13, x14, x15, x23, x24, x25, x34, x35, x45, x21, x31, x41, x51, x32, x42, x52, x43, x53, x54;