A local news channel plans a 36-minute Saturday morning news show. The show will be divided...
A local news channel plans a 36-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 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
x 1 x 2, and x 3 be the number of minutes taken by the sports, news, and weather segments, respectively, and let z be the number of viewers in thousands.
|
Maximize |
z=30x1+75x2+60x3 |
||
|---|---|---|---|
|
subject to |
x1+x2+x3 |
≤ |
36 |
|
−x1 + 2x3 |
≤ |
0 |
|
|
−x1+2x2−x3 |
l≤ |
0 |
|
|
x 1≥0, x 2≥0, x 3≥0. |
|||
The maximum number of viewers is _____
In order to get that number of viewers, there should be ______
minutes of sports,____
minutes of news, and ______minutes of weather.
B) When the viewership is maximized, S1=____ Means that (not all, all) of the available 36 minutes were used, S2=_____means that sports had (exactly, more than, less than) twice as much as the weather, and S3=____means that the sports and weather had a total time (less than, more than, exactly) twice the time of the news.
Homework Answers
Solution using Simplex method is following:
The maximum number of viewers is __1860___
In order to get that number of viewers, there should be __16___ minutes of sports,
__12____ minutes of news, and
___8___minutes of weather.
B) When the viewership is maximized, S1=__0__ Means that all of the available 36 minutes were used, S2=__0___means that sports had exactly twice as much as the weather, and S3=__0__means that the sports and weather had a total time exactly twice the time of the news.
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