Demand, Revenue Functions: rate of change in revenues

[lilcherbear]

Hello,

The marketing department of a computer manufacturer estimates that the demand q (in thousands of units per year) for a laptop is related to price by the demand equation a=200-0.9p. Because of efficiency and technological advances, the prices are falling at a rate of $30 per year (dp/dt=-30). The current price of a laptop is $650. At what rate dR/dt are revenues changing?

I'm ultimately figuring revenue as a function of price instead of as a function of untis. So instead of the normal R(x)...I've got R(p) = 200p-.09p^2 but I am not sure where to go from there. Can you help me?

Thank you
Cherie

 

[stapel]

The marketing department of a computer manufacturer estimates that the demand q (in thousands of units per year) for a laptop is related to price by the demand equation a=200-0.9p. Because of efficiency and technological advances, the prices are falling at a rate of $30 per year (dp/dt=-30). The current price of a laptop is $650. At what rate dR/dt are revenues changing?

I'm not sure what a "normal R(x)" is...? And since nothing in the exercise is defined in terms of x (nor is any definition provided, so I don't know for what x might stand), I'm not sure why you are thinking that it ought to be considered...?

Since the demand q for units is defined in terms of the price p, the revenue, etc, should probably be defined in terms of the variable p. However, I'm not seeing how the variable "a" (in the equation "a = 200 - 0.9p") relates to the demand variable "q"...?

If the revenue is defined as the product of the per-unit price p and the number of units sold (or "demanded") q, then R(p) would be defined as R(p) = pq, where q is the demand function. So once we know how "a" relates to "q", it should be a simple step (plug-n-chug) to find R(p).

Since R is a function of p, and since you are asked for the derivative with respect to time t, you will then differentiate R(p) implicitly with respect to time t. Plug in the given value for dp/dt and the given value for p, and then solve for dR/dt.

If you get stuck, please reply with the missing information and a clear listing of your work and reasoning. Thank you!

Eliz.