The National Collegiate Lacrosse Association is planning its annual national championship tournament.

It selects 16 teams from conference champions and the highest ranked at-large 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 and have been selected based on stadium size and conditions, as well as historical local fan interest in lacrosse. 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.

Game Site Team Rank 1 2 3 4 5 6 7 8 Jackets 1 146 207 361 215 244 192 187 467 Big Red 2 213 0 193 166 312 233 166 631 Knights 3 95 176 348 388 377 245 302 346 Tigers 4 112 243 577 0 179 412 276 489 Bulldogs 5 375 598 112 203 263 307 422 340 Wasps 6 199 156 196 257 389 388 360 288 Blue Jays 7 345 231 207 326 456 276 418 374 Blue Devils 8 417 174 178 442 0 308 541 462 Cavaliers 9 192 706 401 194 523 233 244 446 Rams 10 167 157 233 294 421 272 367 521 Eagles 11 328 428 175 236 278 266 409 239 Beavers 12 405 310 282 278 344 317 256 328 Bears 13 226 268 631 322 393 338 197 297 Hawks 14 284 161 176 267 216 281 0 349 Lions 15 522 209 218 506 667 408 270 501 Panthers 16 197 177 423 183 161 510 344 276

a. Formulate and solve a linear programming model that will assign the teams to the game sites according to the association’s guidelines.

b. Suppose the association wants to consider allowing some flexibility in pairing the teams according to their rankings (i.e., seedings)—for example 1 might play 14 or 2 might play 12—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.