A society of books by correspondence currently has 10000 subscribers who each pa

Question

A society of books by correspondence currently has 10000 subscribers who each pay 50 € per year. A study has shown that an increase (respectively a decrease) of 1 € of the price of the annual subscription, leads to a reduction (respectively an increase) of 100 subscribers.

We propose to find how to change the price of the annual subscription to get the maximum of recipe.ndesignates the variation in the price of the annual subscription in euros and nN.

(a) Express in function of n the price of the annual subscription, and the number of subscribers.

(b) Express the function of n the annual revenue of this company, noted R(n).

(c) Determine the value of n for which R(n) is maximum. What is the amount of the annual subscription, the number of subscribers and the recipe corresponding annual?

Explanation / Answer

Price=50+n

Subscribers=10000-100n

Revenue, R(n)=(50+n)(10000-100n)

dR(n)/dn=10000-100n-100n-5000

For maximum revenue dR(n)/dn=0

5000=200n or n=25

Amount =75€

Number of subscribers=7500

Revenue=75*7500=562500€

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