Channel 999 TV has staff to provide on-scene coverage of up to 4 high school football games this Friday. The following table indicates 3 possibilities are in the town where Channel 999 is located.

At least 2 of them must be covered, as well as at least 1 out of town. The table below shows 4 of the games involve a team likely to compete for the state championship, at least 2 of which must be covered. Games must be fully covered or not at all. Within these requirements Channel 999 wants to maximize its total audience across the ratings points shown for possible game choices.

Game Number 1 2 3 4 5 6 7 8 In town? Y Y Y State champ? Y Y Y Y Ratings points 3.0 3.7 2.6 l.8 l.5 1.3 l.6 2.0

(a) Formulate (but do not solve) a mathematical program to compute optimal choice of games to cover. Be sure to define your decision variables and briefly annotate the objective function, and each

(main or variable-type) constraint with a few words indicating its meaning.

(b) Code your model in AMPL (paralleling Tables 2.6 and 2.7).

(c) Is your model best described as an LP, an ILP, an NLP, or an INLP? Why?