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Universe News is shown on channel X every Friday. During the hour-long broadcast, no more than 17 minutes are allowed to be allocated to commercials. The remaining airtime is allocated to single or multiple time segments for local news, national news, sports, and weather. The advertising revenues generated for commercials shown during the different broadcast segments are different. These are £750 per minute for local news segments, £1000 per minute for national news, £900 per minute for sports, and £900 per minute for the weather. The production cost for local news is £180 per minute, the cost for national news is £140 per minute, the costs for sports is £220 per minute, and for the weather it's £220 per minute. The station budget is £11000 per show for production costs. The station policy is that each of the time segments allocated to local news, national news, and sports should be at least 8% but no more than 46% of the total time allocated to local news, national news, sports, and weather. The time segment allocated to the weather should be at least 7 minutes but no more than 12 minutes long. (Commercials are excluded from these calculations.) Broadcast time devoted to commercials should be at least 5% but no more than 50% of the time segment to which the commercials are added. For example, if the time segment allocated for local news is 10 minutes, then time T of commercials added to this segment should be at least 30 seconds but no more than 300 seconds. So, the total length of this slot will be (10*60+T) seconds.
What is the maximal advertising revenue that the station can gain using an optimal allocation of the time slots?
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