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

Question

Quizplus · Accepted Answer

To maximize profits, we need to find the number of ads that will result in the maximum payment to Jiffy-Pol and subtract the cost of running those ads.

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.

Jiffy-Pol Consultants Is Paid $1,000,000 for Each Percentage of the Vote