Harit Thakuri Staff asked 2 years ago
A politician is trying to win election to the city council, and as his campaign manager, you need to decide how to promote the candidate.
There are three ways you can do so:
a. You can send glossy.full-color pamphlets to registered voters of the city,
b. You can run a commercial during the television news on a local cable network, and /or
c. You can buy a full-page ad in the newspaper.
Two hundred fifty thousand voters live in the city, and 36% of them read the newspaper.
Fifty thousand voters watch the local cable network news, and 30% of them also read the newspaper.
You also know that the television commercial would cost $40,000, the newspaper ad $27,000, and the pamphlets mailed to voters 90 cents each, including printing and bulk-rate postage.
Suppose that the success of the candidate depends on your campaign reaching at least 125,000 voters and that because your budget is limited, you must achieve this goal at a minimum cost. Based on above information, answer the following questions. (Use Venn diagram, if required)
i. How many voters in the city read the newspaper but do not watch the local cable television news?
ii. How many voters read the newspaper or watch the local cable television news, or both?
iii. Complete the following chart by indicating the number of voters reached by each promotional option, the total the cost per voter reached.
iv. What would be your plan and the cost of plan?
There are three ways you can do so:
a. You can send glossy.full-color pamphlets to registered voters of the city,
b. You can run a commercial during the television news on a local cable network, and /or
c. You can buy a full-page ad in the newspaper.
Two hundred fifty thousand voters live in the city, and 36% of them read the newspaper.
Fifty thousand voters watch the local cable network news, and 30% of them also read the newspaper.
You also know that the television commercial would cost $40,000, the newspaper ad $27,000, and the pamphlets mailed to voters 90 cents each, including printing and bulk-rate postage.
Suppose that the success of the candidate depends on your campaign reaching at least 125,000 voters and that because your budget is limited, you must achieve this goal at a minimum cost. Based on above information, answer the following questions. (Use Venn diagram, if required)
i. How many voters in the city read the newspaper but do not watch the local cable television news?
ii. How many voters read the newspaper or watch the local cable television news, or both?
iii. Complete the following chart by indicating the number of voters reached by each promotional option, the total the cost per voter reached.
iv. What would be your plan and the cost of plan?
1 Answers
Harit Thakuri Staff answered 2 years ago
i. To find the number of voters who read the newspaper but do not watch the local cable television news, we can use the information given in the problem. 36% of the 250,000 registered voters read the newspaper, which is:
0.36 x 250,000 = 90,000
30% of the 50,000 voters who watch the local cable news also read the newspaper, which is:
0.30 x 50,000 = 15,000
So, the number of voters who read the newspaper but do not watch the local cable television news is:
90,000 - 15,000 = 75,000
ii. To find the number of voters who read the newspaper or watch the local cable television news, or both, we can use a Venn diagram. Let N represent the set of voters who read the newspaper, and C represent the set of voters who watch the local cable news. The overlap between N and C represents the number of voters who both read the newspaper and watch the local cable news. We can fill in the diagram with the following information:
- 36% of voters read the newspaper, which is 90,000
- 50,000 voters watch the local cable news
- 30% of local cable news viewers also read the newspaper, which is 15,000
- N only = 90,000 - 15,000 = 75,000
- C only = 50,000 - 15,000 = 35,000
- N and C = 15,000
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