DraftKings is an American daily fantasy sports contest and sports betting provider. Daily fantasy sports allow individuals to select players to form a team. In DraftKings Basketball, the team consists of 8 players. That is, one PG, one SG, one Guard (SG or PG), one SF, one PF, one Forward (PF or SF), one Center and one Utility (any position). To require some skill, every player is given a virtual salary. Every entered fantasy must spend less than $50,000. Players receive fantasy points for rebounds, steals, blocks, 2 points, 3 points and assists. Players also lose points for turnovers. The average fantasy points for each player is known. The file "Data - DraftKings Probem.xlsx" is the data for the Friday Feb. 1, 2018 contest (retrieved from https://www.draftkings.com/). This data set does not contain information of players which salary is $3,000 or below since most of them are on the injured list.

a) Formulate an integer programming model to form a team that maximizes the average fantasy points.

b) Solve the integer program using the IBM ILOG CPLEX Optimization Studio.

Players Name Players Team Position Players Salary ($) Game Information Players Average Points per Game Abbreviation Russell Westbrook PG 11600 NO@OKC 02/02/2018 09:00PM ET 57.172 OKC DeMarcus Cousins PF/C 11400 NO @OKC 02/02/2018 09:00PM ET 0.000 NO Anthony Davis PF/C 11400 NO@OKC 02/02/2018 09:00PM ET 50.466 NO Giannis Antetokounmpo SF/PF 10800 NY@MIL 02/02/2018 08:00PM ET 53.656 MIL Stephen Curry PG/SG 10600 GS@SAC 02/02/2018 10:30PM ET 48.111 GS Kevin Durant SF/PF 10400 GS@SAC 02/02/2018 10:30PM ET 47.364 GS Joel Embiid C 9600 MIA@PHI 02/02/2018 08:00PM ET 46.572 PHI Dwight Howard C 9200 IND@CHA 02/02/2018 07:00PM ET 38.220 CHA Kemba Walker PG 8800 IND@CHA 02/02/2018 07:00PM ET 38.932 CHA Kyrie Irving PG 8700 ATL@BOS 02/02/2018 07:30PM ET 40.115 BOS Victor Oladipo PG/SG 8600 IND@CHA 02/02/2018 07:00PM ET 41.707 IND Damian Lillard PG 8500 POR@TOR 02/02/2018 07:30PM ET 43.778 POR Kristaps Porzingis PF/C 8300 NY@MIL 02/02/2018 08:00PM ET 39.506 NY Draymond Green F/C 3200 GS@SAC 02/02/2018 10:30PM ET 37.205 GS Ben Simmons PG/SF 8100 MIA@PHI 02/02/2018 08:00PM ET 41.729 PHI Rudy Gobert C 8000 UTA@PHO 02/02/2018 09:00PM ET 32.000 UTA Hassan Whiteside C 7900 MIA@PHI 02/02/2018 08:00PM ET 35.182 VIA Donovan Mitchell PG/SG 7800 UTA@PHO 02/02/2018 09:00PM ET 32.266 UTA DeMar DeRozan SG/SF 7700 POR@TOR 02/02/2018 07:30PM ET 39.577 TOR Jrue Holiday PG/SG 7700 NO@OKC 02/02/2018 09:00PM ET 35.880 NO Devin Booker PG/SG 7600 UTA@PHO 02/02/2018 09:00PM ET 39.152 PHO Al Horford PF/C 7600 ATL@BOS 02/02/2018 07:30PM ET 34.601 BOS CJ Mccollum PG/SG 7500 POR@TOR 02/02/2018 07:30PM ET 35.055 POR Paul George SF 7400 NO@OKC 02/02/2018 09:00PM ET 38.260 OKC Khris Middleton SG/SF 7300 NY@MIL 02/02/2018 08:00PM ET 36.311 MIL Kyle Lowry PG 7200 POR@TOR 02/02/2018 07:30PM ET 37.196 TOR Goran Dragic PG 7000 MIA@PHI 02/02/2018 08:00PM ET 31.016 MIA Enes Kanter PF/C 6900 NY@MIL 02/02/2018 08:00PM ET 30.954 NY Lonzo Ball PG 6800 LAL@BKN 02/02/2018 07:30PM ET 34.618 LAL Brandon Ingram SG/SF 6800 LAL@BKN 02/02/2018 07:30PM ET 29.652 LAL Dennis Schroder PG 6700 ATL@BOS 02/02/2018 07:30PM ET 34.750 ATL Klay Thompson SG 6700 GS@SAC 02/02/2018 10:30PM ET 32.705 GS Spencer Dinwiddie PG/SG 6700 LAL@BKN 02/02/2018 07:30PM ET 28.827 BKN Julius Randle PF/C 6700 LAL@BKN 02/02/2018 07:30PM ET 27.555 LAL T.J. Warren SF/PF 6600 UTA@PHO 02/02/2018 09:00PM ET 31.413 PHO Steven Adams C 6600 NO@OKC 02/02/2018 09:00PM ET 30.788 OKC Terry Rozier PG/SG 6600 ATL@BOS 02/02/2018 07:30PM ET 21.192 BOS