A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 13x - 0.025x² The variable x is measured in thousands of toys produced, and r (x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?

Question

Houston Kelley

Mathematics

20 December, 02:30

A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 13x - 0.025x² The variable x is measured in thousands of toys produced, and r (x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?

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Teagan Andersen · Answer 1

R (x) = 13x - 0.025x^2

For maximum R, R' (x) = 0

R' (x) = 13 - 0.05x = 0

0.05x = 13

x = 13/0.05 = 260

R (260) = 13 (260) - 0.025 (260) ^2 = 3380 - 1690 = 1690

Maximum revenue = $1,690,000