Revenue function, profit function, domain

Question

Suppose the demand price for selling out a production run of x DVDs is given by p(x)=-0.0005x^2+60 dollars per DVD.

Further suppose the weekly cost of producing these DVDs is given by C(x)=-0.001x^2+18x+4000 dollars to produce that many DVDs.

(i) Write the Revenue function R(x). And be sure to state its DOMAIN.

(ii) Use (i) to write the profit function P(x). Again, be sure to state its DOMAIN.

(iii) Draw a signs diagram for p'(x), the marginal profit function. Here you will first need to solve p'(x)=0 by using the quadratic formula

I am very confused as to how to get the domain in these problems because initially I thought it was (-infinity, infinity) for both revenue function and profit function, but my professor said that mathematically this is correct, but since we're talking about the real world it would be something else and it wouldn't make sense to have negative infinity, and I would like an explanation as to how to get the domain. Would the interval be (0, infinity) for both, or is there a method to figuring out the domain in this situation.

Answer 1

Revenue = (price)(quantity). So, R(x) = x(0.0005x²+60), where x > 0

Profit = Revenue - Cost. So, P(x) = R(x) - C(x), where x > 0