A local news channel plans a 45-minute Saturday morning news show. The show will be divided into three segments involving sports, news, and weather. Market research has shown that the sports segment should be at least twice as long as the weather segment. The total time taken by the sports and weather segments should be at least twice the time taken by the news segment. On the basis of the market research, it is believed that 30, 75, and 60 (in thousands) viewers will watch the program for each minute the sports, news, and weather segments, respectively, are on the air. Use the simplex method to complete parts (a) and (b). (a) Find the time that should be allotted to each segment in order to get the maximum number of viewers. Find the number of viewers. Set up the linear programming problem. Let x₁, x₂, and x3 be the number of minutes taken by the sports, news, and weather segments, respectively, and let z be the number of viewers in thousands. subject to X₁ + x₂ + x3 x. +2x. ▼

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