A political party is planning a ninety-minute television show. The show will have at least 9 minutes of direct requests for money from viewers. Three of the party's politicians will be on the show- a senator, a congresswoman, and a governor. The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor. The total time taken by the senator and the governor must be at least twice the time taken by the congresswoman. Based on a pre-show survey, it is believed that 37, 41, and 45 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers. Find the maximum number of viewers. The quantity to be maximized, z, is the number of viewers in thousands. Let x, be the total number of minutes allotted to the senator, × be the total number of minutes allotted to the congresswoman, and x3 be the total number of minutes allotted to the governor. What is the objective function? Z= 37 x1 + 41 X2 + 45 x3 A.The senator should be allotted………..minutes. B. The congresswoman should be allotted…….minutes. C. The governor should be allotted ………..minutes. D.The maximum number of viewers is ……….. .

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter8: Evolutionary Solver: An Alternative Optimization Procedure

Section8.8: Optimal Permutation Models

Problem 15P

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A political party is planning a ninety-minute television show. The show will have at least 9 minutes of direct requests for money from viewers. Three of the party's politicians will be on the show- a senator, a congresswoman, and a governor. The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor. The total time taken by the senator and the governor must be at least twice the time taken by the congresswoman. Based on a pre-show survey, it is believed that 37, 41, and 45 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers. Find the maximum number of viewers. The quantity to be maximized, z, is the number of viewers in thousands. Let x, be the total number of minutes allotted to the senator, × be the total number of minutes allotted to the congresswoman, and x3 be the total number of minutes allotted to the governor. What is the objective function? Z= 37 x1 + 41 X2 + 45 x3 A.The senator should be allotted………..minutes. B. The congresswoman should be allotted…….minutes. C. The governor should be allotted ………..minutes. D.The maximum number of viewers is ……….. .

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Decision Variable:

$S u p p o s e - x_{1} b e t h e m i n u t e s a l l o t t e d t o t h e s e n a t o r x_{2} b e t h e m i n u t e s a l l o t t e d t o t h e c o n g r e s s w o m a n x_{3} b e t h e m i n u t e s a l l o t t e d t o t h e g o v e r n o r$

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