A television station has commercials of the following lengths (in seconds): 15, 20, 25, 30, 40, 45, 50, and 60. The commercials must be assigned to 90-second breaks. If a commercial break exceeds 90 seconds, a penalty cost is incurred. Station managers have established a penalty of $100 (per second) if the maximum limit is exceeded. Moreover, station owners want commercial breaks that are at least 65 seconds in duration. If any break fails to achieve this minimum duration, then a $1000 penalty (per occurrence) is charged. What is the fewest number of breaks that are needed to air all eight of the commercials?
A television station has commercials of the following lengths (in seconds): 15, 20, 25, 30, 40, 45, 50, and 60. The commercials must be assigned to 90-second breaks. If a commercial break exceeds 90 seconds, a penalty cost is incurred. Station managers have established a penalty of $100 (per second) if the maximum limit is exceeded. Moreover, station owners want commercial breaks that are at least 65 seconds in duration. If any break fails to achieve this minimum duration, then a $1000 penalty (per occurrence) is charged. What is the fewest number of breaks that are needed to air all eight of the commercials?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 73P
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A television station has commercials of the following lengths (in seconds): 15, 20, 25, 30, 40, 45, 50, and 60. The commercials must be assigned to 90-second breaks. If a commercial break exceeds 90 seconds, a penalty cost is incurred. Station managers have established a penalty of $100 (per second) if the maximum limit is exceeded. Moreover, station owners want commercial breaks that are at least 65 seconds in duration. If any break fails to achieve this minimum duration, then a $1000 penalty (per occurrence) is charged. What is the fewest number of breaks that are needed to air all eight of the commercials?
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