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/minute for local news and feature story segments, $600/minute for national news, $750/minute for sports, and $1000/minute for the weather. The production cost for local news is $400/minute, the cost for national news is $100/minute, for sports the cost is $175/minute and for weather it is $90/minute. The station budgets $9000 per show for production costs. The station’spolicy is that the broadcast time devoted to local news and
features must be at least 10 minutes but no more than 25 minutes while national news, sports, and weather must each have segments of at least 5 minutes but no 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 in order to maximize advertising revenues. Formulate and solve a linear programming model for this problem.