SOLUTION: Word problem: A local newspaper that circulates daily. They have 80,000 subscribers in circulation. Currently the price is $1.50 per week and it is estimated that the paper would

Question 813333: Word problem:
A local newspaper that circulates daily. They have 80,000 subscribers in circulation. Currently the price is $1.50 per week and it is estimated that the paper would lose 5,000 subscribers if the rate were to be raised by 10 cents per week. Find the subscription price that would maximize the profits. Also, consider the following:
1) Fluctuation of Lost Subscribers
2) Fluctuation of Current Price
3) Fluctuation of Raised Cost
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Word problem:
A local newspaper that circulates daily. They have 80,000 subscribers in circulation. Currently the price is $1.50 per week and it is estimated that the paper would lose 5,000 subscribers if the rate were to be raised by 10 cents per week. Find the subscription price that would maximize the profits. Also, consider the following:
1) Fluctuation of Lost Subscribers
2) Fluctuation of Current Price
3) Fluctuation of Raised Cost
--------------------
Revenue = (# of subscribers)(price per unit)
---
R(x) = (80,000-5000x)(1.50+0.10x)
----
= 5000(16-x)(0.1)(15+x)
----
= 500(-x^2+x+240)
----
Max occurs when x = -b/(2a) = -1/(-2) = 0.5
----
Max subscription occurs when the price is raised by 5 cents
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Cheers,
Stan H.
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