Question

A company's revenue from selling x units of an item is given as R=1600x−x^2 If sales are increasing at the rate of 40 units per day, how rapidly is revenue increasing (in dollars per day) when 250 units have been sold?

___ dollars per day

Answer 1

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Answer
Sales are increasing at the rate of 40 units per day . X is the number of units inthe question .X depends on days(time ).
therefore ,
dx/dt = 40 (rate of change in units per day)

We need to find dr /dt (change in revenue per day)

Revenue depends on x (units) and x depends on t .Therefore we find dr/dt by substituting dx/dt

R=1600x-x2
dr/dt = 1600 dx/dt -2x dx/dt

When x= 250

dr/dt = 1600(40)-2(250)(40)
= 64000-20000
=44000 $ per day

Revenue is increasing by 44000 per day when 250 units have been sold.