The Boston Red Sox major league baseball team decided to study which game starting times they should utilize in the next season. One way to approach this scheduling problem is to conduct a large survey of people who watch television and ask if they would watch a game starting at a particular time on a given day of the week. As an example of the data, see the matrix below where each row corresponds to a survey respondent and each column corresponds to a proposed day and start time (WN = week night, Sat = Saturday, and Sun = Sunday). All starting times are p.m. A “1” indicates the person prefers to watch a game starting at that time and a “0” indicates the person does not prefer a game at that time.

We must choose one weeknight starting time and one starting time each for Saturday and Sunday. Sponsorship revenue for the televised games is dependent on viewership measured by the number of viewers who will watch at least one game per week.
The file gametimes contains data from 75 respondents.

a. Develop a binary integer linear model to select starting times to maximize the number of viewers for whom at least one of their preferred times have been chosen.

b. Create a spreadsheet model of your model in part (a) and solve it using Excel Solver.

c. Give the optimal starting times and the optimal number of viewers who watch at least one game per week.

Transcribed Image Text:

WN WN Sat Sat Sat Sun Sun Sun Respondent 6:30 7:30 2:00 6:00 8:00 2:00 4:00 7:30 1 1 1 1 1 0 0 0 1 23 4 2 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 5 0 0 1 0 0 1 1 1