Five students A, B, C, D, & E have been shortlisted to represent the University in a case competition. The question is which students to choose for the competition. The selection committee has to consider the cost, as all students have to travel from their respective homes to the site of the competition in Calgary. The costs for the students travel are $900, $1,100, $2,200, $800, & $1,500, & their prospects of winning have been estimated on the basis of their grades as 0.59, 0.35, 0.72, 0.15, & 0.41, respectively.

(a) Define your decision variables & formulate a problem that maximizes the overall prospects of winning by our team subject to a budget constraint that ensures that no more than $2,500 can be spent.

(b) Formulate constraint that choose no more than three students for the competition.

(c) Formulate constraint that if student E is not chosen, then student D must be chosen.

(d) Formulate constraint that both student B and C must be chosen or neither be chosen.

(e) Formulate constraint that if student A is chosen, then student E must not be chosen.