L 04 (Total 28 marks) Eye-on-Earth News is shown on TV Channel 3 Monday through Friday evenings from 4:00pm to 5:00pm. During the hour-long broadcast, 10 minutes are allocated to commercials. The remaining 50 minutes of airtime are allocated to single or multiple programs for local news, national news, local features, entertainment, sports, and, weather. To provide more variety of program to the audiences, at least 5 programs should be selected. The advertising revenues generated during the different broadcast segments are $850 per minute for local news segments, $550 per minute for national news, $620 per minute for local features, $1,000 per minute for entertainment, $750 per minute for sports, and $950 per minute for the weather. The variable production cost for local news is $400 per minute, national news is $180 per minute, local features is $120 per minute, entertainment is $130 per minute, sports is $175 per minute, and weather is $125 per minute. The fixed production cost will incur once the program is selected. The fixed production cost for local news, national news, local features, entertainment, sports, and, weather are $1,000, $1,000, $1,950, $1,800, $1,100 and $1,350 respectively. The following policy on broadcasting time of program should be considered: Broadcasting time can be allocated only if the program is selected. If local news is selected, its broadcast time must be at least 15 minutes. If weather is selected, it must have segment no more than 8 minutes. If national news is selected, its broadcast time must be at least 8 minutes, but no more than 16 minutes. If sports is selected, its broadcast time must be at least 5 minutes, but no more than 15 minutes. Maximum 10 minutes can be allocated to entertainment. - In addition, at least 10% of total broadcast time should be allocated for local features and sports together. Broadcast time for national news should no more than the total broadcast time for local features, and, entertainment. The total broadcast time for entertainment and weather must be at least twice as great as the total broadcast time for local features and sports. The station manager wants to know which program should be selected and how many minutes of broadcast time to allocate to each program to maximize total profit. (a) Formulate a linear programming model for this problem. (20 marks)