Question

Please help i really dont know how to start.

Answer 1

(a) The monthly revenue is given by the function
`R(x) = x \cdot p(x)`, and we are given that
`p(x) = 5 - 0.001x`. So, we have


`R(x) = x (5 - 0.001x) = 5x - 0.001 x^2`.

(b) The monthly profit is given by the function
`P(x) = R(x) - C(x)`, and we are given that
`C(x) = 35 + 1.5x`. So, we have


`P(x) = (5x - 0.001x^2) - (35 + 1.5x) = 3.5x - 0.001x^2 - 35`.

(c) We already have the formula for P(x), so you can just plug in the values:
x = 600, x = 1200, x = 1800, etc. into P(x) and write down the answers.

The trickier part is finding the derivatives. We'll start with dR/dx:

`(dR)/(dx) = (d)/(dx)[5x - 0.001x^2] = 5 - 0.002x`.

The next is dP/dx:

`(dP)/(dx) = (d)/(dx)[3.5x - 0.001x^2 - 35] = 3.5 - 0.002x - 0 = 3.5 - 0.002x`.

Once again, just plug in the different values of x into the formulas we found and we will be able to complete the table.

If you're confused on how I calculated the derivatives, let me know. I made the assumption that you already knew how to do that (although that is not always true). :)