A businessman models the number of items (in thousands) that his company sold from 1998 through 2002 as N (x) = - 0.2x3 + x2 - 2x + 9 and the average price per item (in dollars) as P (x) = 0.6x + 5, where x represents the number of years since 1998. Enter a polynomial R (x) that can be used to model the total revenue for this company.

Question

Mercer

Mathematics

30 September, 20:00

A businessman models the number of items (in thousands) that his company sold from 1998 through 2002 as N (x) = - 0.2x3 + x2 - 2x + 9 and the average price per item (in dollars) as P (x) = 0.6x + 5, where x represents the number of years since 1998. Enter a polynomial R (x) that can be used to model the total revenue for this company.

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Jacqueline Thompson · Answer 1

Basically, you are asked to find the equation for total revenue. In economics, total revenue is equal to the the quantity multiplied with price.

Total Revenue = Price*Quantity

Thus,

R (x) = P (x) * N (x)

R (x) = (0.6x + 5) (-0.2x ³ + x ² - 2x + 9)

R (x) = - 0.12x ⁴ + 0.6x³ - 0.12x² + 5.4x - x³ + 5x² - 10x + 45

R (x) = - 0.12x⁴ - 0.4x³ + 4.88x² - 4.6x + 45