The program manager for KWTV Channel 8 would like to determine the best way to allocate the time for the 11:00–11:30 evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 30-minute broadcast, 10 minutes are set aside for advertising. The station’s broadcast policy states that at least 15% of the time available should be devoted to local news coverage; the time devoted to the combination of local news and national news must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment; the time devoted to the sports segment should be no longer than the total time spent on the local and national news; and at least 20% of the time should be devoted to the weather segment. The production costs per minute are $300 for local news, $200 for national news, $100 for weather, and $100 for sports.
The program manager for KWTV Channel 8 would like to determine the best way to allocate the time for the 11:00–11:30 evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 30-minute broadcast, 10 minutes are set aside for advertising. The station’s broadcast policy states that at least 15% of the time available should be devoted to local news coverage; the time devoted to the combination of local news and national news must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment; the time devoted to the sports segment should be no longer than the total time spent on the local and national news; and at least 20% of the time should be devoted to the weather segment. The production costs per minute are $300 for local news, $200 for national news, $100 for weather, and $100 for sports.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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The program manager for KWTV Channel 8 would like to determine the best way to allocate the time for the 11:00–11:30 evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather, and sports. Over the 30-minute broadcast, 10 minutes are set aside for advertising. The station’s broadcast policy states that at least 15% of the time available should be devoted to local news coverage; the time devoted to the combination of local news and national news must be at least 50% of the total broadcast time; the time devoted to the weather segment must be less than or equal to the time devoted to the sports segment; the time devoted to the sports segment should be no longer than the total time spent on the local and national news; and at least 20% of the time should be devoted to the weather segment. The production costs per minute are $300 for local news, $200 for national news, $100 for weather, and $100 for sports.
Transcribed Image Text:The program manager for KWTV Channel 8 would like to determine the best way to allocate the
time for the 11:00-11:30 evening news broadcast. Specifically, she would like to determine the
number of minutes of broadcast time to devote to local news, national news, weather, and sports.
Over the 30-minute broadcast, 10 minutes are set aside for advertising. The station's broadcast
policy states that at least 15% of the time available should be devoted to local news coverage; the
time devoted to the combination of local news and national news must be at least 50% of the total
broadcast time; the time devoted to the weather segment must be less than or equal to the time
devoted to the sports segment; the time devoted to the sports segment should be no longer than
the total time spent on the local and national news; and at least 20% of the time should be devoted
to the weather segment. The production costs per minute are $300 for local news, $200 for national
news, $100 for weather, and $100 for sports.
Please save your file as firstinitial_Lastname_OPT06.xlsx
(E.g., for Bill Wright, save file as b_wright_ OPT06.xlsx)
A. Formulate the algebraic model for a linear program to determine how the 20 available minutes
should be used to minimize the total cost of producing the program.
B. Using Excel Solver, determine the time allocation plan for that results in a optimal solution.
C. Interpret the shadow price for the constraint corresponding to the available time. What advice
would you give the station manager given this shadow price?
D. Interpret the shadow price for the constraint corresponding to the requirement that at least 15%
of the available time should be devoted to local coverage. What advice would you give the
station manager given this shadow price?
E. Interpret the shadow price for the constraint corresponding to the requirement that the time
devoted to the weather segment must be less than or equal to the time devoted to the sports
segment. What advice would you give the station manager given this shadow price
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