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University of Waterloo
Combinatorics and Optimization
CO 250
Christine Dupont

1. A company can form 4 teams of experts. These teams can then earn a certain amount of revenue for the company. There are 6 experts that the company can hire. Each expert charges a retainer fee if they work for the company. Due to what the teams do, certain teams MUST have certain experts, shown in the following table (x indicates the expert MUST be in that team): Expert Revenue 1 2 3 4 5 6 (in $) Team 1 x x x 1000 2 x x x 800 3 x x x x 1100 4 x x x x x 900 Retainer Fee (in $) 800 500 300 300 600 500 Each expert can be on at most two teams. Formulate an integer program to determine what teams should be formed to maximize pro▯t. 2. UW is seeking to choose its board of trustees. There are eight candidates available for selection who come from various backgrounds. UW has listed the three main attributes of each candidate: (a) Region (Kitchener/Waterloo) (b) Profession (Academics/Industry) (c) Politics (Liberal/Conservative) that are relevant for the selection process in the table below. The table also gives an as- sessment of the funding (in 1000s of $) that each candidate may bring to UW if s
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