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Answer :
Final answer:
The bookstore's daily revenue, with Amazon.com and BN.com each earning $5,000, depends on BooksAMillion.com's revenue as R(z) = 9,850 - 0.00995z.
Explanation:
The student has provided a function for the major online bookstore's daily revenue, R(x,y,z), which is dependent upon the daily revenues of Amazon.com, BN.com, and BooksAMillion.com. The task is to provide an equation representing the bookstore's daily revenue based only on the daily revenue of BooksAMillion.com, given fixed revenues for Amazon.com and BN.com.
Given the provided revenue function and the fixed daily revenues for Amazon.com and BN.com, which are $5,000 each, we can substitute these values into the equation:
R(x,y,z) = 10,000 - 0.01x - 0.02y - 0.01z + 0.00001yz
Substituting the fixed revenues we get:
R(z) = 10,000 - 0.01(5,000) - 0.02(5,000) - 0.01z + 0.00001(5,000)z
Simplifying further:
R(z) = 10,000 - 50 - 100 - 0.01z + 0.00005z
Combining like terms:
R(z) = 9,850 - 0.00995z
This equation represents the online bookstore's daily revenue depending solely on BooksAMillion.com's revenue.
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Final answer:
The equation showing how the daily revenue of the online bookstore depends on the daily revenue of BooksAMillion.com is R(z) = 9,850 + 0.04z.
Explanation:
To find an equation showing how the daily revenue of the online bookstore depends on the daily revenue of BooksAMillion.com, we need to substitute the given values for Amazon.com and BN.com into the revenue function and simplify the equation.
Given: x = $5,000 (daily revenue of Amazon.com)
y = $5,000 (daily revenue of BN.com)
Substituting these values into the revenue function, we get:
R(z) = 10,000 - 0.01(5,000) - 0.02(5,000) - 0.01z + 0.00001(5,000)z
Simplifying the equation:
R(z) = 10,000 - 50 - 100 - 0.01z + 0.05z
R(z) = 9,850 - 0.01z + 0.05z
R(z) = 9,850 + 0.04z
Therefore, the equation showing how the daily revenue of the online bookstore depends on the daily revenue of BooksAMillion.com is R(z) = 9,850 + 0.04z.
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