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 50, 70, 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 -X₁ + 2x3 -X₁+2x2-x3 x₁20, X₂20, X3 20. (Do not factor.) 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. (Type whole numbers.) (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. When viewership is maximized, s, - means that of the available 36 minutes were used; s2 - twice as much time as the weather; and s3 - means that the sports and the weather had a total time the time of the news. (Type whole numbers.) means that sports had twice
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 50, 70, 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 -X₁ + 2x3 -X₁+2x2-x3 x₁20, X₂20, X3 20. (Do not factor.) 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. (Type whole numbers.) (b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem. When viewership is maximized, s, - means that of the available 36 minutes were used; s2 - twice as much time as the weather; and s3 - means that the sports and the weather had a total time the time of the news. (Type whole numbers.) means that sports had twice
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 50, 70, 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
-X₁ + 2x3
-X₁+2x2-x3
x₁20, X₂20, x3 20.
(Do not factor.)
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.
(Type whole numbers.)
(b) Explain what the values of the slack variables in the optimal solution mean in the context of the problem.
When viewership is maximized, s, - means that
twice as much time as the weather; and s3 - means that the sports and the weather had a total time
the time of the news.
(Type whole numbers.)
of the available 36 minutes were used; s2 = means that sports had
twice
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