Silo State’s School of Engineering is preparing a 5-year plan for building construction and expansion to accommodate new offices, laboratories, and classrooms. The Electrical Engineering faculty has proposed projects for all 3 available parcels of land: a digital circuits lab on the northwest parcel at $48 million, a faculty office annex on the southeast parcel at $20.8 million, and a computer vision lab on the northeast parcel at $32 million. The Mechanical Engineering faculty has 3 alternative proposals for the same northwest parcel: a large lecture room building at $28 million, a heat transfer lab at $44 million, and a computer-aided design expansion at $17.2 million. The Industrial Engineering faculty has only 2 proposals: a manufacturing research center on the southeast parcel at $36.8 million, and a tunnel from their current building to the new center for an additional $1.2 million. The Dean of Engineering scores the impact of these projects as 9, 2, and 10 for the EE proposals, 2, 5, and 8 for the ME alternatives, 10 and 1 for the IE ideas.

He wishes to allocate his available $100 million to maximize the total impact, selecting projects on an all-or-nothing basis with at most one per land parcel.

(a) Describe verbally the budget limits, mutual exclusiveness constraints, and project dependency requirements of this capital budgeting problem.

(b) Formulate a capital budgeting ILP to select an optimal combination of proposals.

(c) Use class optimization software to solve your ILP model.