John White is the program scheduling manager for the television channel CCFO. John would like to...

  

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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 $ millions) 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. Number 1 2 3 4 5 6 7 8 9 Show Sam's Place Texas Oil Cincinnati Law Jarred Bob & Mary Chainsaw Loving Life Islanders Urban Sprawl Revenue ($ millions) Public Interest Violent Comedy Drama $8 $11 $12 $6 $7 $4 $8 $10 $9 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 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: Consideration 1: Exactly 5 television shows must be selected. Consideration 2: The schedule must include at least as many shows that are categorized as public interest as shows that are categorized as violent. Consideration 3: If John schedules "Loving Life," then he must also schedule either "Jarred" or "Cincinnati Law" (or both). Consideration 4: John cannot schedule both "Loving Life" and "Urban Sprawl." Consideration 5: 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. [1 if show iis selected for i = 1, 2, 3, 4, 5, 6, 7, 8, 9. Let y = 1 if two or more violent movies (a) Formulate a binary integer program that models the decisions John faces. Let x = 0 otherwise x are chosen and 0 otherwise. Give your objective function in millions of dollars. For Consideration 5, use the smallest (in magnitude) possible integer coefficient for y.) 1 if show i is selected for i = 1, 2, 3, 4, 5, 6, 7, 8, 9. Let y = 1 if two or more violent movies Let x, = 0 otherwise (a) Formulate a binary integer program that models the decisions John faces. are chosen and 0 otherwise. Give your objective function in millions of dollars. For Consideration 5, use the smallest (in magnitude) possible integer coefficient for y.) Min s.t. Consideration 1 Consideration 2 Consideration 3. Consideration 4 Consideration 5 (b) Solve the model formulated in part (a). (X11 X2 X3 X4 X5, X61 X71 Xgr Xgr Y) = ( What is the optimal revenue (in millions of dollars)? million 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 $ millions) 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. Number 1 2 3 4 5 6 7 8 9 Show Sam's Place Texas Oil Cincinnati Law Jarred Bob & Mary Chainsaw Loving Life Islanders Urban Sprawl Revenue ($ millions) Public Interest Violent Comedy Drama $8 $11 $12 $6 $7 $4 $8 $10 $9 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 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: Consideration 1: Exactly 5 television shows must be selected. Consideration 2: The schedule must include at least as many shows that are categorized as public interest as shows that are categorized as violent. Consideration 3: If John schedules "Loving Life," then he must also schedule either "Jarred" or "Cincinnati Law" (or both). Consideration 4: John cannot schedule both "Loving Life" and "Urban Sprawl." Consideration 5: 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. [1 if show iis selected for i = 1, 2, 3, 4, 5, 6, 7, 8, 9. Let y = 1 if two or more violent movies (a) Formulate a binary integer program that models the decisions John faces. Let x = 0 otherwise x are chosen and 0 otherwise. Give your objective function in millions of dollars. For Consideration 5, use the smallest (in magnitude) possible integer coefficient for y.) 1 if show i is selected for i = 1, 2, 3, 4, 5, 6, 7, 8, 9. Let y = 1 if two or more violent movies Let x, = 0 otherwise (a) Formulate a binary integer program that models the decisions John faces. are chosen and 0 otherwise. Give your objective function in millions of dollars. For Consideration 5, use the smallest (in magnitude) possible integer coefficient for y.) Min s.t. Consideration 1 Consideration 2 Consideration 3. Consideration 4 Consideration 5 (b) Solve the model formulated in part (a). (X11 X2 X3 X4 X5, X61 X71 Xgr Xgr Y) = ( What is the optimal revenue (in millions of dollars)? million

Answer rating: 100% (QA)

To formulate the binary integer program based on Johns decisions we need to create a model with binary variables xi for each show i where xi 1 if show ... View the full answer