Related Rate (Calculus)

Question

A company's revenue from selling x units of an item is given as R=1300x−3x^2. If sales are increasing at the rate of 45 units per day, how rapidly is revenue increasing (in dollars per day) when 150 units have been sold?

Answer 1

Sales are the number of items sold (x) so the rate that sales are increasing is dx/dt. We are being asked to find the rate that revenue is increasing, or dR/dt

Take the revenue equation, R = 1300x − 3x² and take the derivative with respect to time. You must use the chain rule:

dR/dt = (1300)(dx/dt) - (6x)(dx/dt)

we know dx/dt = 45 and we know x = 150 so:

dR/dt = (1300)(45) - (6)(150)(45) = 18000 (the units would be $/day)