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 :" 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 Brad Greene 55 6'10 ' Center For the starting line- up , either Jonathan Galloway , Collin Welp or Brad Greene can be included ;" 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 instead ?" 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" difference to 6 feet " to build the objective function