Asked by Kaila Martinez on May 07, 2024
Verified
Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election.Sleaze's share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S 100N/(N 1) , where N is the number of ads.If each ad costs $10,000 approximately how many ads should Jiffy-Pol buy in order to maximize its profits?
A) 200
B) 1,995
C) 999
D) 1,099
E) 500
Slanderous Campaign Ads
Defamatory or malicious advertising used especially during political campaigns to harm the reputation of an opposing candidate.
Vote Determination
The process by which preferences or decisions are expressed and counted, often within the context of elections or decision-making bodies, to decide outcomes.
Profit Maximization
The method through which a company identifies the pricing and production quantity that yields the highest profit.
- Interpret the strategy for enhancing business earnings in multiple scenarios.
- Assess the effect of advertising and its related expenses on the optimization of profits.
Verified Answer
First, we need to determine the percentage of the vote Senator Sleaze will receive for each number of ads run. Plugging in different values of N into the function, we get:
N = 1: S = 50%
N = 2: S = 66.67%
N = 3: S = 75%
N = 4: S = 80%
N = 5: S = 83.33%
N = 6: S = 85.71%
N = 7: S = 87.5%
N = 8: S = 88.89%
As we can see, adding more ads increases the percentage of the vote, but at a decreasing rate.
Next, we need to determine the payment to Jiffy-Pol for each number of ads run. We do this by multiplying the percentage of the vote by $1,000,000:
N = 1: Payment = $500,000
N = 2: Payment = $666,667
N = 3: Payment = $750,000
N = 4: Payment = $800,000
N = 5: Payment = $833,333
N = 6: Payment = $857,143
N = 7: Payment = $875,000
N = 8: Payment = $888,889
Finally, we subtract the cost of running the ads ($10,000 per ad) from the payment to Jiffy-Pol to get the profit:
N = 1: Profit = $490,000
N = 2: Profit = $656,667
N = 3: Profit = $740,000
N = 4: Profit = $760,000
N = 5: Profit = $823,333
N = 6: Profit = $797,143
N = 7: Profit = $865,000
N = 8: Profit = $848,889
Therefore, the optimal number of ads to run is 999 (choice C), which results in a profit of $900,000. Running more ads does increase the percentage of the vote for Senator Sleaze, but at a decreasing rate, so the additional revenue does not outweigh the cost of the ads.
Learning Objectives
- Interpret the strategy for enhancing business earnings in multiple scenarios.
- Assess the effect of advertising and its related expenses on the optimization of profits.
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