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 twice as long as the weather segment. The total time taken by the sports and weather segments should be twice the time taken by the news segment. On the basis of the market research, it is believed that 40, 65, 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.
The maximum number of viewers is BLANK. In order to get that number of viewers, there should be BLANK minutes of sports, BLANK minutes of news, and BLANK minutes of weather.
My TI-84 calculator broke and I don't understand the textbook. Could someone explain how I can solve this question?
So far, I have:
Maximize z = 40x1 + 65x2 + 60 x3
subject to x1 + x2 + x3 ≤ 45
−x1 + 2x3 ≤ 0
−x1 + 2x2 − x3 ≤ 0
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
Simplex tableau:
[ 1 1 1 1 0 0 45]
[ -1 0 2 0 1 0 0]
[ -1 2 -1 0 0 1 0]
[ 40 65 60 0 0 0 ]
draw the lines that form the boundary of the region of constraints.
Evaluate z at each vertex.
Pick the largest value.