The National Collegiate Lacrosse Association is planning its annual national championship tournament. It selects the top 16 teams to play in the single-elimination tournament. The teams are ranked from 1 (best) to 16 (worst), and in the first round of the tournament, the association wants to pair the teams so that high-ranked teams play low-ranked teams (i.e., seed them so that 1 plays 16, 2 plays 15, etc.). The eight first-round game sites are predetermined. Because of limited school budgets for lacrosse and a desire to boost game attendance, the association wants to assign teams to game sites so that all schools will have to travel the least amount possible. The following table shows the 16 teams in order of their ranking and the distance (in miles) for each of the teams to each of the eight game sites.

b) Suppose the association wants to consider allowing flexibility in pairing teams (so that any team could play against any other) in order to see to what extent overall team travel might be reduced. Reformulate and solve the model to see what effect this might have. (12 points)

Team Rank 6 Jackets Big Red Knights Tigers Bulldogs Wasps Blue Jays Blue Devils Cavaliers Rams Eagles Beavers 1 2 3 146 207 361 213 0 193 95 176 348 112 243 577 375 598 112 199 156 196 345 231 207 417 174 178 192706 401 167 157 233 328 428 175 405 310 282 226 268 631 284 161 176 522 209 218 197 177 423 Game Site 4 5 215 244 166 312 388 377 0 179 203 263 257 257 389 326 4 56 442 0 194 523 294 421 236 278 278 344 322 393 267 216 506 667 183 161 6 192 233 245 412 307 388 276 308 233 272 266 317 338 281 408 510 7 8 187 467 166 631 302 346 276489 422 340 360 288 418 374 541462 244 446 367 521 409 239 256 328 197 297 0 349 270 501 3 44 276 10 Bears Hawks 13 14 15 16 Lions Panthers Team Rank 6 Jackets Big Red Knights Tigers Bulldogs Wasps Blue Jays Blue Devils Cavaliers Rams Eagles Beavers 1 2 3 146 207 361 213 0 193 95 176 348 112 243 577 375 598 112 199 156 196 345 231 207 417 174 178 192706 401 167 157 233 328 428 175 405 310 282 226 268 631 284 161 176 522 209 218 197 177 423 Game Site 4 5 215 244 166 312 388 377 0 179 203 263 257 257 389 326 4 56 442 0 194 523 294 421 236 278 278 344 322 393 267 216 506 667 183 161 6 192 233 245 412 307 388 276 308 233 272 266 317 338 281 408 510 7 8 187 467 166 631 302 346 276489 422 340 360 288 418 374 541462 244 446 367 521 409 239 256 328 197 297 0 349 270 501 3 44 276 10 Bears Hawks 13 14 15 16 Lions Panthers