Question

In a particular county in the State of Arkansas, four election issues are on the ballot: Build new highways, increase gun control, increase farm subsidies, and increase gasoline tax. The county includes 100,000 urban voters, 250,000 suburban voters, and 50,000 rural voters, all with varying degrees of support for and opposition to election issues. For example, rural voters are opposed to gun control and gas tax and in favor of road building and farm subsidies. The county is planning a TV advertising campaign with a budget of $100,000 at the cost of $1,500 per ad. The following table summarizes the impact of a single ad in terms of the number of pro and con votes as a function of the different issues:

	Expected number of pro(+) and con (−) votes per ad
Issue	Urban	Suburban	Rural
New highways	−30,000	+60,000	+30,000
Gun control	+80,000	+30,000	−45,000
Farm subsidies	+40,000	+10,000	0
Gas tax	+90,000	0	−25,000

An issue will be adopted if it garners at least 51% of the voters. Which issues will be approved by voters and how many ads should be allocated to these issues?

Answer 1

ANSWER

Total number of votes=100000+250000+50000=400000

Total number of votes required =0.51*400000=204000

a)

Net Votes in 1 ad for New Highway=-3000+60000+30000=60000 votes

Total number of advertising allotted= Total number of votes required/ Net Votes in 1 advertisement

Total number of advertising allotted=204000/60000=3.4

Total number of advertising allotted=3.4

b)

Net Votes in 1 ad for Gas control=+80000+30000-45000=65000 votes

Total number of advertising allotted= Total number of votes required/ Net Votes in 1 advertisement

Total number of advertising allotted=204000/65000=3.13

Total number of advertising allotted=3.13

c)

Net Votes in 1 ad for Smog control=+40000+10000-0=50000 votes

Total number of advertising allotted= Total number of votes required/ Net Votes in 1 advertisement

Total number of advertising allotted=204000/50000=4.08

Total number of advertising allotted=4.08

d)

Net Votes in 1 ad for Gas tax=+90000+0-25000=65000 votes

Total number of advertising allotted= Total number of votes required/ Net Votes in 1 advertisement

Total number of advertising allotted=204000/65000=3.13

Total number of advertising allotted=3.13

Since total number of advertisement required is minimum in b) Gas control and d) Gas tax

Thus the issues of Gas control and Gas tax will be adopted by the voter

And the number of ads allocated to this issue will be 3.13 ads

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