After a season in which he made extensive use of all 12 players on his team, a coach is trying to select the starting team for postseason tournament play. The following are the season statistics on the players:

 

Player	Position	Height	Rebounds	Points	Assists	FGA	FTA	Turnovers	Fouls
Dave	Guard	70	1.3	1.6	3.3	58	90	2.1	3.2
Al	Guard	72	1.3	3.2	4.5	53	85	1.2	2.1
Tom	Guard	69	2.8	12.1	2.2	47	70	3.3	1.2
Joe	Guard	73	3.3	3.2	3.6	41	72	2.0	2.4
Paul	Guard	68	1.1	9.6	2.0	42	68	2.2	3.4
Sean	Forward	76	7.7	6.7	2.2	38	70	2.8	4.1
Ron	Forward	75	4.5	13.0	2.7	49	75	1.5	2.1
Bob	Forward	77	2.0	15.6	2.8	52	85	4.0	3.0
Jim	Forward	79	7.5	16.2	2.3	47	60	2.1	2.2
Ben	Center	80	3.0	3.9	4.8	45	65	2.3	2.2
Herb	Center	82	8.9	12.8	1.0	40	60	1.0	3.6
John	Center	83	5.0	8.2	1.2	56	88	2.2	1.9

 

In choosing his starting team the coach has 8 goals he would like to meet.  They are:

 

1.Average starting team height at least 75 inches.

2.Total team average rebounds per game at least 24.

3.Total team average points per game at least 58.

4.Total team average assists per game at least 13.

5.Team field goal average (FGA) at least 50.

6.Team free throw goal average (FTA) at least 75.

7.Total team average turnovers per game no more than 11.

8.Total team average fouls per game no more than 12.

 

The coach also wishes to impose the following restriction on the starting team:

 

1.At least one guard must start

2.Exactly one center must start.

3.If either Al or Ron start, Jim cannot start.

 

Create a Solver-based spreadsheet model based on goal programming methods to determine which players should start and solve the model.