The Maryland Basketball Association (MBA) has identified 20 top players in its north division whose initials and current stats are given below (PPG = points per game; REB = rebounds per game; AST = assists per game). The north division needs to select a team of 10 players for its All-Star game against the south division. The following are nuances of the MBA:

• A full game comprises of two halves.

• 5 players will play the first half and 5 will play the second half.

• A player, if selected, plays a full half.

• A player can NOT play both halves. Coach K, MBA-North’s coach for the All-Star game, knows that the team has a high probability of winning if he maximizes the total number of points scored. However, he also knows that the best way to improve his chances is to have a balanced approach where the team also records at least 18 rebounds and 18 assists in each half. [Assume that each player’s stats are representative of their performance of an entire game and that there is no statistical difference in performance between the two halves]

What player mix, by half, will you recommend to Coach K? Construct and solve an Integer Programming model consisting of binary variables to determine the selected players and the halves in which they will play. [Suggestion: First create three additional columns and calculate the stats per half.]

 

Player PPG REB AST BB 31 4.8 4.8 SC 30.7 5.5 5.9 DL 28.7 4.2 7.7 GA 28.5 11.2 6.1 LD 28.4 7.9 8.8 KI 27.5 4.8 6.1 ZV 27.5 5.1 5.1 ZW 26.7 7.1 3.6 DM 26.4 4.4 5.2 NJ 26.1 11 8.8 KL 26 6.6 5 DB 25.7 4.2 4.5 JT 25.6 7.1 4.2 LJ 25.4 7.9 7.9 DF 25.2 3.5 7.1 JH 25.2 8 10.9 TY 25.2 3.9 9.5 JB 24.6 5.8 3.4 BI 24.3 4.8 CS 24.2 2.8 4.1