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

Answer:

The daily rate is: 17500 units per day

Step-by-step explanation:

Given

$R = 1700x - 2x^2$

$\frac{dx}{dt} = 25$

Required

Find $\frac{dR}{dt}$ when $x = 250$

We have:

$R = 1700x - 2x^2$

Differentiate both sides with respect to time

$\frac{dR}{dt} = 1700\frac{dx}{dt} - 4x\frac{dx}{dt}$

Factorize

$\frac{dR}{dt} = (1700- 4x)\frac{dx}{dt}$

Substitute: $\frac{dx}{dt} = 25$ and $x = 250$

$\frac{dR}{dt} = (1700- 4x)\frac{dx}{dt}$

$\frac{dR}{dt} = (1700- 4*250)*25$

$\frac{dR}{dt} = (1700- 1000)*25$

$\frac{dR}{dt} = 700*25$

$\frac{dR}{dt} = 17500$