Question

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 − 0.01z + 0.00001yz,
where x, y, and z are the online daily revenues of Amazon.com, BN.com, and BooksAMillion.com respectively

If, on a certain day, Amazon.com shows revenue of $14,000, while BN.com and BooksAMillion.com each show $6,000, what does the model predict for your company's revenue that day?

Answer 1

Using the revenue model R(x, y, z), the predicted revenue for the student's company, with Amazon.com at $14,000 and both BN.com and BooksAMillion.com at $6,000 each, is calculated to be $9,683.60 for that particular day.

Step-by-step explanation:

To find your company's daily revenue using the given model R(x, y, z) = 10,000 - 0.01x - 0.02y - 0.01z + 0.00001yz, where x, y, and z are the online daily revenues of Amazon.com, BN.com, and BooksAMillion.com respectively, we need to plug in the values provided for a certain day.

On that day, Amazon.com (x) has a revenue of $14,000, BN.com (y) and BooksAMillion.com (z) each have a revenue of $6,000. Plugging these values into the model gives:

R(14,000, 6,000, 6,000) = 10,000 - 0.01(14,000) - 0.02(6,000) - 0.01(6,000) + 0.00001(6,000)(6,000)

The calculation results in R(14,000, 6,000, 6,000) = 10,000 - 140 - 120 - 60 + 3.6 = 9,683.6. Therefore, the model predicts that your company's revenue for that day would be $9,683.60.