Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com. Your company's daily revenue in dollars is given by:

\[ R(x, y, z) = 10,000 - 0.01x - 0.02y - 0.012z + 0.00001yz \]

where $ x, y, $ and $ z $ are the online daily revenues of Amazon.com, BN.com, and BooksAMillion.com, respectively.

(a) If, on a certain day, Amazon.com shows revenue of $12,000, while BN.com and BooksAMillion.com each show $4,000, what does the model predict for your company's revenue that day?

(b) If Amazon.com and BN.com each show daily revenue of $4,000, give an equation showing how your daily revenue depends on that of BooksAMillion.com. $ R(z) = $

The model predicts that the company's revenue on the given day would be approximately $9,799.988. The equation showing how the company's daily revenue depends on that of BooksAMillion.com is R(z) = 9,879.988 + 0.00001z.

Explanation:

To calculate the company's revenue on a certain day, we need to substitute the given values into the revenue model equation R(x, y, z) = 10,000 – 0.01x – 0.02y – 0.012 + 0.00001yz.

(a) If Amazon.com shows revenue of $12,000, while BN.com and BooksAMillion.com each show $4,000, we substitute x = 12,000, y = 4,000, and z = 4,000 into the equation:

R(12,000, 4,000, 4,000) = 10,000 - 0.01(12,000) - 0.02(4,000) - 0.012 + 0.00001(4,000)(4,000)

Simplifying the equation:

R(12,000, 4,000, 4,000) = 10,000 - 120 - 80 - 0.012 + 0.00001(16,000,000)

R(12,000, 4,000, 4,000) = 9,799.988

Therefore, the model predicts that the company's revenue on that day would be $9,799.988.

(b) If Amazon.com and BN.com each show daily revenue of $4,000, we substitute x = 4,000 and y = 4,000 into the equation:

R(4,000, 4,000, z) = 10,000 - 0.01(4,000) - 0.02(4,000) - 0.012 + 0.00001(4,000)z

Simplifying the equation:

R(4,000, 4,000, z) = 10,000 - 40 - 80 - 0.012 + 0.00001(4,000)z

R(4,000, 4,000, z) = 9,879.988 + 0.00001z

Therefore, the equation showing how the company's daily revenue depends on that of BooksAMillion.com is R(z) = 9,879.988 + 0.00001z.

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