Question

WILL MEDAL AND FAN!! PLEASE HELP?????
The revenue R (in dollars) from renting x apartments can be modeled by
R = 2x(700 + 34x − x^2).
(a) Find the additional revenue when the number of rentals is increased from 14 to 15.
$ _________

(b) Find the marginal revenue when x = 14.
$ _________

(c) Compare the results of parts (a) and (b).
The answers are close.
The answers are not close.

Answer 1

is that \(2 \times (700 + 34x -x^2)\) , i.e 2 times ( ... )
or \(2x(700 +34x-x^2)\), i.e. 2x times ( ...)

Answer 2

it's 2x not 2 times

Answer 3

for a), you can find the revenue for x=14, and for x=15, and subtract off the two revenues.

\(R_{14} = 2(14)(700 + 34(14) − (14)^2)\)
\(R_{15} = 2(15)(700 + 34(15) − (15)^2)\)
Then find the value \(R_{15}-R_{14}\)

Answer 4

is it 2110?

Answer 5

yes

Answer 6

Marginal revenue then for b)
is finding \(R\,'_{14}\), so the derivative evaluated at x = 14
\[\large R\,' _{14} =\left.\frac{d}{dx}2x(700+34x-x^2)\right|_{x=14}=\left.\frac{d}{dx}(1400x+68x^2-2x^3)\right|_{x=14}\\
=\large \left. 1400+68(2)x-2(3)x^2\right|_{x=14}=1400+68(2)(14)-2(3)(14)^2\]

Answer 7

so part b is 2120?

Answer 8

so part c would be close but not equal?

Answer 9

i get 2128

Answer 10

i suppose they would be considered close

Answer 11

aww.. well they are still close and it really helped you walking me through this Thank you!

Answer 12

:) yw