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(answered) - Doug Davis, programming manager for Spike-TV, must plan h


Doug Davis, programming manager for Spike-TV, must plan his schedule of television shows for next Wednesday evening. Of the nine one-half hour shows listed below, he must select exactly five for Wednesday evening. The estimated revenue (in $ million) is given below for each show. Furthermore, the F.C.C. has classified each show as falling into one or more of the categories of Public Interest, Violence, Comedy, and Drama as given in the table below.

ID #

Show

Revenue ($mill)

Public Interest

Violent

Comedy

Drama

1

2

3

Modern Family

Ghost

Scorpion

7

6

8

X

X

X

X

X

X

X

4

5

6

Walking Dead

TroubleMakers

Triumph

5

8

3

X

X

X

X

X

X

7

8

9

Jokers

China Beach

Mentalist

4

7

2

X

X

X

X

X

Doug?s task is to select exactly five shows in order to maximize revenue. However, he must be mindful of the following limitations and issues:

There must be at least as many shows aired that are categorized as drama as there are shows aired that are categorized as comedy.

He cannot air more than two of the shows "Triumph", "Jokers" and "Mentalist" (too serious!).

If Doug airs "Jokers", she must air either "Walking Dead" or "Scorpion" but not both.

If he airs four or more shows in the violence category, she pays F.C.C. a fine of $5 million, which will be deduced from the revenue.

Formulate Doug Davis?s selection problem as a binary optimization problem. Clearly define your decision variables, constraints, and objective function. Use only linear constraints and a linear objective function. You do not have to solve the model in Excel.


Our objective is to maximise profit by broadcasting exactly 5 shows with highest revenues on Wednesday evening,

 

provided that follwing conditions are satisfied:

 

1)

 

There must be atleast as many...

 


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