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Answer :
Final answer:
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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