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

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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(53937)   (Show Source):
You can put this solution on YOUR website!
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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

Solved.

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On finding the maximum/minimum of a quadratic function see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola

Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Learn the subject from there once and for all.

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