Professor Proof is trying to decide which of 6 needed teaching assistant tasks he will assign to each of his 2 graduate assistants. Naturally, one assistant would probably be better at some tasks and the other assistant better at others. The following table shows his scoring of their potentials

(high is good).

Assistant Task 1 2 3 4 5 6 0 100 85 40 45 70 82 1 80 70 90 85 80 65 Professor Proof wants to assign three tasks to each assistant. However, tasks 5 and 6 are related and should be assigned to the same assistant.

(a) Explain why appropriate decision variables for an optimization model of this problem are 1j = 1,c, 62 xj! e 0 if task j is assigned to 0 1 if task j is assigned to 1

(b) Formulate an objective function to maximize the potential of the assignment chosen.

(Hint: 1 - xj = 1 when xj = 0.)

(c) Formulate a single main constraint to enforce requirements that at each assistant be assigned three tasks.

(d) Formulate a single main constraint to enforce the requirement that tasks 5 and 6 go to the same assistant.

(e) Complete your model with an appropriate system of variable-type constraints.

(f) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective? Explain.

(g) Enter and solve your model with class optimization software.