3. Eyewitness News is shown in channel 5 Monday through Friday evenings from 5:00 P.M. to 6:00 P.M. During the hour long broadcast, at most 18 minutes of airtime are allocated to commercials. The remaining airtime (in minutes) 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 local weather than the national news (because they know that 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, $1000 per minute for weather. The production cost for local news is $400 per minute, the cost for nation news is $100 per minute, the cost for sports is $175 per minute, and for weather it's $90 per minute. The station budgets $9000 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 each have segments of at least 5 minutes but not more than 10 minutes. Commercial time must be limited to no more than 6 minutes for each of the for broad cast types. (a) Formulate a linear programming model that helps the station manager to max- imize the advertising revenues subject to production budget constraint. Define