Question

In: Operations Management

The program manager for Channel 10 would like to determine the best way to allocate the...

The program manager for Channel 10 would like to determine the best way to allocate the time available for the 11:00 PM to 11:30 PM evening news broadcast. Specifically, she wants 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 leaving the remaining time for the news broadcast. The station is a member of a national broadcasting company that has established the following guidelines on scheduling.

1) At least 15% of the available time must be devoted to local news

2) Local or national news must make up at least 50% of the broadcast time.

3) The time devoted to weather must be less than or equal to the time devoted to sports.

4) The total time devoted to sports cannot exceed the time allocated to local and national news (view this as only 1 segment).

5) At least 20% of the time must be devoted to weather.

The cost of production for each minute is $300 for local news, $200 for national news, $100 for weather, and $100 for sports. (Hint: don’t forget all the available time must be used)

The variables used in this problem are: L for local news, N for national news, W for weather, and S for sports.

  1. How much time should be allocated to local news? How much time allocated to national news? How much time allocated to weather? How much time allocated to sports?

b) What is the minimum cost of producing the news broadcast?

c) Since there are 10 minutes of advertising in the news broadcast what is the lowest amount that the program manager must charge for one minute of advertising?

Solutions

Expert Solution

Formulation:

Min Z = 300 L + 200 N + 100 W + 100 S
s.t.
L + N + W + S = 20 (Total available time)
L >= 0.15 of 20 i.e. 3 (Requirement-1)
L + N >= 0.50 of 20 i.e. 10 (Requirement-2)
W - S <= 0 (Requirement-3)
S - L - N <= 0 (Requirement-4)
W >= 0.20 of 20 i.e. 4 (Requirement-5)
L, N, W, S >= 0

--------------------

LINDO Code

Min 300 L + 200 N + 100 W + 100 S
s.t.
L + N + W + S = 20
L > 3
L + N > 10
W - S < 0
S - L - N < 0
W > 4
end

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Solution:

-----------------

(a)

How much time should be allocated to local news? L = 3 minutes
How much time allocated to national news? N = 7 minutes
How much time allocated to weather? W = 5 minutes
How much time allocated to sports? S = 5 minutes

(b)

Min Cost = $3,300

(c)

As per the range report, the dual price for the first constraint is -100. So, if one more minute is available, the cost will reduce by $100. So the changes for one minute of advertisement should be this opportunity loss i.e. $100.

keosha answered 5 months ago
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