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# 1. The UCI man basketball team is trying to choose its starting line-up from their roster for their first game on the 2019 Asia Pacific University...

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1 . The UCI man basketball team is trying to choose it's starting line-up from their roster for their
first game on the 2019 Asia Pacific University Basketball Challenge so as to maximize average
height . The roster follows :&quot;
Player
Number| Height Position
JC Butler
615'
Forward
Devin Cole
1
5'1 1'
Guard
Max Hazzard
2
6'0'
Guard
Robert Cartwright
3
Guard
Aiden Krause
4
6'4'
Guard
Jonathan Galloway
5
6'10'\
Forward
John Edgar Jr.
1 1
6'5'
Forward
Evan Leonard
14
Guard
Darrian Traylor
23
Guard
Eyassu Worku
24
612'
Guard
Spencer Rivers
25
612'
Guard
Solomon Ruddell*
35
7'1'
Center
Collin Welp
40
6'9''
Forward
Tommy Rutherford
42
618'
Forward
Elston Jones
50
6'9''
Forward
55
6'10 '
Center
For the starting line- up , either Jonathan Galloway , Collin Welp or Brad Greene can be included ;&quot;
also , only one center might start ; and finally if John Edgar Jr. or Robert Cartwright starts , then Brad
Greene cannot start . Take those requirements into account to ,
a ) Help Coach Turner to determine the optimal starting line - up if the classical two guards , two
forwards , and one center is selected .
b ) Would that optimal line - up change if three guards , one forward , and one center is selected
C ) What about if at most one center , but otherwise any combination of positions is allowable ?
For each of the cases , specify the respective integer program , the solution and it's interpretation .
Note : I foot = 12 inches . Also it is easier you consider height as&quot; difference to 6 feet &quot; to build the
objective function .

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