The Blue Hills Home Corporation (BHHC)15 employs 22 remedial education teachers to service special needs students at 22 schools in the St. Louis area. BHHC assigns its teachers to schools for an entire year and is presently making decisions for the current year. One assignment consideration is cost; BHHC reimburses its teachers the cost ci, j of teacher i traveling to school j. However, the assignment must also consider 3 sets of preferences. Teachers express preferences scores ti, j of teacher i being assigned to school j, BHHC supervisors express preferences si, j, and school principals provide scores pi, j. In all three cases a higher score indicates a greater preference.

(a) Explain why appropriate decision variables for a mathematical programming model of this problem are 1i, j = 1,c, 222 xi, je 1 if teacher i is assigned to school j 0 otherwise

(b) Using these decision variables and the symbolic input constants above, express all BHHC assignment goals as separate objective func tions.

(c) Write a system of 22 constraints expressing the requirement that each teacher be assigned to exactly one school.

(d) Write a system of 22 constraints expressing the requirement that each school be assigned exactly one teacher.

(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.