Question 1) The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function.
C(x) = 2000 + 2x - 0.0001x2 (0 ≤ x ≤ 6000)
(a) What is the actual cost incurred in producing the 921st and the 2071st disc?
(b) What is the marginal cost when x = 920 and 2070?
Question 2) Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function, where C(x) is measured in dollars/year.
C(x) = 90x + 230000
(a) Find the average cost function C-.
(b) Find the marginal average cost function C-'?
(c) What happens to C-(x) when x is very large?
Question 3) Williams Commuter Air Service realizes a monthly revenue represented by the following function, where R(x) is measured in dollars and the price charged per passenger is x dollars.
R(x) = 6400x - 80x2
(a) Find the marginal revenue R'(x).
(b) Compute the following values.
R'(39)=
R'(40)=
R'(41)=
(c) Based on the results of part (b), what price should the airline charge in order to maximize their revenue?
Question 4)Pulsar also manufactures a series of 20-in. flat-tube digital televisions. The quantity x of these sets demanded each week is related to the wholesale unit price p by the following equation.
p = -0.067x + 250
The weekly total cost incurred by Pulsar for producing x sets is represented by the following equation.
C(x) = 0.000006x3 - 0.07x2 + 400x + 87000
(a) Find the revenue function R.
Find the profit function P.
(b) Find the marginal cost function C'.
Find the marginal revenue function R'.
Find the marginal profit function P'.
(c) Complete the following values.
C'(1300)=
R'(1300)=
P'(1300)=