Marginal income. The demand equation is p = f (x) and the income function is given by R (x) = px = xf (x)

ACME company management plans to commercialize Electro-Stat fans. The marketing department has determined the demand for the fans is:

p=?0.03x+800 (0x20000)

Where p denotes unit price in dollars, and x the quantity demanded.

A. Determine the income function R (x)

B. Determine the marginal revenue function R (x)

C. Calculate R '(3000) and interpret the result

Marginal profit. Using the information from the previous problem. If the Electro-Stat fan production department estimates that the total dollar cost of producing x systems in one year will be:

C(x)=200x+600000)

Profit function (profit) = P (x) = R (x) -C (x) = (Profit = Revenues-cost)

Remember that the revenue function (R (x) or revenues) you defined in the previous problem.

a. Determine the profit function (Profit) P (x)

b. Determine the marginal profit function P (x)

c. Calculate P (2000) and interpret result