Eyewitness News is shown on channel 5 Monday through Friday evenings from 5:00 P.M. to 6:00 P.M. During the hour-long broadcast, 18 minutes are allocated to commercials. The remaining 42 minutes of airtime are allocated to single or multiple time segments for local news and features, national news, sports, and weather. The station has learned through several viewer surveys that viewers do not consistently watch the entire news program; they focus on some segments more closely than others. For example, they tend to pay more attention to the local weather than the national news (because they know they will watch the network news following the local broadcast). As such, the advertising revenues generated for commercials shown during the different broadcast segments are $850 per minute for local news and feature segments, $600 per minute for national news, $750 per minute for sports, and $1,000 per minute for the weather. The production cost for local news is $400 per minute, the cost for national news is $100 per minute, the cost for sports is $175 per minute, and for weather it's $90 per minute. The station budgets $9,000 per show for production costs. The station's policy is that the broadcast time devoted to local news and features must be at least 10 minutes but not more than 25 minutes, whereas national news, sports, and weather must have segments of at least 5 minutes each but not more than 10 minutes. Commercial time must be limited to no more than 6 minutes for each of the four broadcast segment types. The station manager wants to know how many minutes of commercial time and broadcast time to allocate to local news, national news, sports, and weather to maximize advertising revenues.
a. Formulate a linear programming model for this problem.
b. Solve by using the computer.