BASKETBALL TEAM SELCECTION BY GOAL PROGRAMMING After a season in which he made e
ID: 468929 • Letter: B
Question
BASKETBALL TEAM SELCECTION BY GOAL PROGRAMMING
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.
Comments and Hints:
1.For those unfamiliar with basketball, exactly five players must be selected.
2.For those unfamiliar with basketball, it is desirable to overachieve the first 6 goals and desirable to underachieve the final 2 goals. This is implied in the wording of the goal statements.
Take care when calculating actual values for the goals, noting the sumproduct calculation must be divided by 5 for goals 1, 5 and
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
Explanation / Answer
Selecting a starting team - Let's check who fits to the goal criteria
Number of team members to be selected for the starting team are - 5
1) Average starting team height should be atleast 75 inches - This means the average team height of all the five players together should be atleast 75. As per this criteria, the players who take part in the team are : almost all. Almost everybody is eligible. But the members we could select from the best of the lot are
Average of these five is 77.2 which is matching the criteria
2) Total team average rebounds per game is at least 24
Total team average rebounds is 23.2 which is not satisfying the goal criteria. So all those who are eligible for the criteria are : Al, Jim, Herb, John, Ron
3) Total team average points per game is at least 58
Total team average points - 61.7 which is matching the goal criteria
4) Total team average assists per game is at least 13
9.9 is the total average points of the team which is not satisfying the goal criteria. All those satisfying the criteria are - Ben, Jim, Ron, Bob, Al
5) FGA should be at least 50
48.8 is not satisfying.
6) FTA average is 75
Tom, Ron, Bob, Herb, John are meeting the criteria
7) Total average team turnovers not more than 11
Al, Tom, Ron, Herb, John, are meeting the criteria
8) Total team average fouls not more than 12
Al, Tom, Ron, Bob, John are meeting the criteria
The team should be, Al, John, Tom, Herb, Ron out of which
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