Question

A company decides to begin making and selling computers. The price function is given as follows:
p=−70x+4000,

where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial department has determined that the weekly fixed cost of production will be 3000 dollars with an additional cost of 250 dollars per unit.
(A) Find the revenue function in terms of x.
R(x) =
(B) Use the financial department's estimates to determine the cost function in terms of x.
C(x) =
(C) Find the profit function in terms of x.
P(x) =
(D) Evaluate the marginal profit at x=250.
P′(250) =

Answer 1

r(x) = -70x+4000
c(x) = 3000 + 250x
p(x) = r(x)-c(x) = -320x

Answer 2

The first is incorrect.
R(x) = x(-70x+4000) = -70x^2 +4000x
P(x) = (-70x^2 +4000x) - (3000+250x) = -70x^2 + 3750x - 3000
Dunno what the first person was thinking but these should be correct. :)

Answer 3

Oh and for the last part just get the derivative for P(x)
P'(x)= -140x + 3750
Then plug in 250 for x
P'(250)= -140(250) +3750 = -31250