John White is the program scheduling manager for the television channel CCFO. John would like to plan the schedule of television shows for next Wednesday evening. The table below lists nine shows under consideration. John must select exactly five of these shows for the period from 8:00 p.m. to 10:30 p.m. next Wednesday evening. For each television show, the estimated advertising revenue (in $ million) is provided. Furthermore, each show has been categorized into one or more of the categories “Public Interest,” “Violent,” “Comedy,” and “Drama.” In the following table, a 1 indicates that the show is in the corresponding category and a 0 indicates it is not.
John would like to determine a revenue-maximizing schedule of television shows for next Wednesday evening. However, he must be mindful of the following considerations:
••The schedule must include at least as many shows that are categorized as public interest as shows that are categorized as violent.
••If John schedules “Loving Life,” then he must also schedule either “Jarred” or “Cincinnati Law” (or both).
••John cannot schedule both “Loving Life” and “Urban Sprawl.”
••If John schedules more than one show in the “Violent” category, he will lose an estimated $4 million in advertising revenues from family-oriented sponsors.
a. Formulate a binary integer program that models the decisions John faces.
b. Solve the model formulated in part (a). What is the optimal revenue?