A university needs to put together a committee to handle
students’ complaints. To ensure that all perspectives are represented, it is
necessary to have a diverse committee by including at least one female, one
male, one student, one administrator and one faculty member. Ten individuals
have been nominated but since it is important to maintain the anonymity of the
committee, the individuals are identified by the letters A to J. The mix of
individuals in the different categories is given as follows:

Category Individual

Females A, B, C, D, E

Males F, G, H, I, J

Students A, B, C, J

Administrators E, F

Faculty D, G,H, I

The university wants to form the smallest committee possible
with representation from each of the five categories.

a) Formulate a linear mathematical model to find the optimal
solution and put it in standard format. Clearly define your decisions
variables, objective function and constraints

b) Implement your model in Excel and use Solver to find the
optimal solution. Include a snapshot of your answer in the report

c) If individuals (A) and (F) do not get along, and
therefore, we cannot have them together on the committee, what would be the new
linear constraint that can model this condition? Just include the constraint
without repeating the whole formulation and remember that the model must remain
linear (i.e., no IF-THEN or similar functions are allowed). Implement this
additional condition in Excel and provide the new solution.

d) Suppose that in addition to the condition in part (c),
faculty member (I) may have to decline joining the committee due to a project
commitment, in which case student (A) must also decline to be on the project
with her professor. What would be the new linear constraint that can model this
condition? Just include the constraint without repeating the whole formulation
and remember that the model must remain linear (i.e., no IF-THEN or similar
functions are allowed). Implement this additional condition in Excel and
provide the new solution.