SOLUTION: The Art of Problem Solving has begun selling a cookbook called "What Would Euler Eat?" If the price of the cookbook is n dollars (n \le 10), then it will sell 100 - 10n copies. W
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Question 1209304: The Art of Problem Solving has begun selling a cookbook called "What Would Euler Eat?" If the price of the cookbook is n dollars (n \le 10), then it will sell 100 - 10n copies. What price per book (in dollars) will maximize the total revenue we receive for all the books sold? Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! .
The Art of Problem Solving has begun selling a cookbook called "What Would Euler Eat?"
If the price of the cookbook is n dollars (n <= 10), then it will sell 100 - 10n copies.
What price per book (in dollars) will maximize the total revenue we receive for all the books sold?
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At n <= 10, the total revenue is
R(n) = n*(10-n) = 10n - n^2.
This formula represent a downward parabola, so it has a maximum.
The maximum/(the vertex) is at n = , where "a" is the coefficient at n^2,
"b" is the coefficient at n
= = = 5.
The revenue is maximum at n= 5 dollars. ANSWER
