Question

A company's revenue from selling x units of an item is given as R=1700x-2x^2 . If sales are increasing at the rate of 25 units per day, how rapidly is revenue increasing ( in dollars per day ) when 250 units have been sold

Answer 1

The daily rate is: 17500 units per day

Explanation:

Given

`R = 1700x - 2x^2`

`(dx)/(dt) = 25`

Required

Find
`(dR)/(dt)` when
`x = 250`

We have:

`R = 1700x - 2x^2`

Differentiate both sides with respect to time

`(dR)/(dt) = 1700(dx)/(dt) - 4x(dx)/(dt)`

Factorize

`(dR)/(dt) = (1700- 4x)(dx)/(dt)`

Substitute:
`(dx)/(dt) = 25` and
`x = 250`

`(dR)/(dt) = (1700- 4x)(dx)/(dt)`

`(dR)/(dt) = (1700- 4*250)*25`

`(dR)/(dt) = (1700- 1000)*25`

`(dR)/(dt) = 700*25`

`(dR)/(dt) = 17500`