The university is putting together three task forces to consider various changes to the governance structure of three faculties. A handful of members have been pre$-$selected to form these teams and the university has tasked you with putting these three teams together. Each team should have each faculty represented and should be about equal in the average age of the group. In addition, each group must contain at least one member whose primary language is French and another whose primary language is English. Finally, due to interpersonal conflict on previous committees it is deemed prudent that Candidate $1$ not be placed in the same group as Candidate $7.$ The information required is provided in the table below.

Candidate Language Faculty $2013$ Performance

$1$ French Science $33$

$2$ English Science $65$

$3$ English Telfer $53$

$4$ English Telfer $49$

$5$ French Engineering $27$

$6$ French Engineering $62$

$7$ English Engineering $35$

$8$ French Telfer $54$

$9$ French Science $41$

$10$ French Telfer $43$

$11$ English Engineering $55$

$12$ French Science $32$

Provide the LP formulation for this problem and solve to provide the optimal solution. Submit an Excel file with your formulation together with an answer report. $($Hint: try creating the objective as a goal program where the goal for each task force is to get the average age as close to the average age of all candidates.$)$