Problem B (30 points)The program manager, Matt Simon, for TV Channel 25 would like to determine the best way to allocate the time for the 11:00-11:30 evening news broadcast. He would like to know the most profitable way to allocate broadcast time to local news, national news, weather, and sports. Over the thirty-minute broadcast, no more than ten minutes can be set aside for commercial advertising which generates the sole profit at a rate of $2500 per minute. The station's broadcast policy states that at least 15% of the time available should be devoted to local news coverage; the time devoted to local news and national news combined must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to sports segment; the time devoted to the sports segment should be no longer than the combined time spent on the local and national news; and at least 18% of the broadcast time should be devoted to the weather segment. The production costs per minute are $300 for local news, $200 for national news, $120 for weather, and $100 for sports.

1. Formulate a linear programming model to help Mr. Matt Simon with his managerial problem at Channel 25.