(20 points) The coach of the HK men's basketball team has to select a team of 5 players from 9 players. The details of the 9 players are shown in the following table: Formulate a binary integer programming problem to select the team with the highest total average points per game, subject to the following restrictions: - The team must include at least 1 center and 2 guards. Also, the team must not include more than 2 forwards. - The average assists per game of the team must be at least 6 . The average defensive ability of the team must be at least 5 . The average height of the team must be at least 174cm. - Player 1 would not join the team if Player 9 is selected. - Player 3 and Player 6 would only join the team if both of them are selected