The programme manager for Channel SABC II would like to determine the best way to allocate the time for the 19:00 to 19:30 evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 30-minute time slot, 10 minutes are set aside for advertising and do not count as broadcast time. The station policy states the following:
• At least 15% of the broadcast time should be devoted to local news coverage;
• The time devoted to local or national news (combined) must be at least 50% of the broadcast time.
• The time devoted to the weather segment must be less than or equal to the time devoted to the sports segment.
• The time devoted to the sports segment should be no longer than the total time spent on local and national news (combined) and
• At least 20% of the broadcast time should be devoted to the weather segment.
The production costs/minute are R4500 for local, R3 000 for national, R1 500 for weather, and R1 500 for sports.
Formulate an LP model that can be used to determine how many of minutes to assign to each type of programme to minimise the cost. Do not solve the model.
