Question

**Marginal Cost**

The total weekly cost (in dollars) incurred by Lincoln Records
in pressing *x* compact discs is given by the following
function.

*C*(*x*) = 2000 + 2*x* −
0.0001*x*^{2} (0 ≤ *x*
≤ 6000)

(a)

What is the actual cost incurred in producing the 1071st and the 1991st disc? (Round your answers to the nearest cent.)

1071st disc$ 1991st disc$

(b)

What is the marginal cost when *x* = 1070 and 1990?
(Round your answers to the nearest cent.)

1070$ 1990$

Answer #1

The weekly cost (in dollars) of producing x compact discs is
given by
C(x) = 2000 + 2x − 0.0001x^2
,
where x stands for the number of units produced. What is the
actual cost incurred in producing
the 2001st disc? What is the marginal cost when x = 2000?

The weekly cost (in dollars) of producing x compact discs is
given by C(x) = 2000 + 2x − 0.0001x^2,
where x stands for the number of units produced. What is the
actual cost incurred in producing the 1001st disc? What is the
marginal cost when x = 1000?

The weekly demand for DVDs manufactured by a certain media
corporation is given by
p = −0.0004x2 + 70
where p denotes the unit price in dollars and
x denotes the quantity demanded. The weekly total cost
function associated with producing these discs is given by
C(x) = −0.001x2 + 19x + 4000
where C(x) denotes the total cost (in dollars)
incurred in pressing x discs. Find the production level
that will yield a maximum profit for the manufacturer.
Hint:...

1. Suppose the total weekly cost (in dollars) of producing x
fuel tanks is given by 2 C x x x ( ) 12,000 80 0.04 = + − for x in
the interval (0,1500)
a) Over what intervals will the total weekly cost be increasing
and when will it be decreasing?
Increasing: _______________________ Decreasing:
_________________________
b) When will the total weekly cost be at its max and what will
the maximum cost be? State answer using appropriate units.
Solution:...

Acrosonic's production department estimates that the total cost
(in dollars) incurred in manufacturing x ElectroStat
speaker systems in the first year of production will be represented
by the following function, where R(x) is the
revenue function in dollars and x denotes the quantity
demanded. Find the following functions (in dollars) and compute the
values (in dollars).
C(x) = 110x +
27,000 and R(x)
= −0.04x2 + 800x
(a)Find the profit function P.
(b)Find the marginal profit function P '.
(c)Compute the following...

Suppose that the cost (in dollars) for a company to produce
x pairs of a new line of jeans is described by the formula
below.
C(x) = 5000 +
2x + 0.03x2 +
0.0002x3
(a) Find the marginal cost function.
C'(x) =
(b) Find C'(50).
(c) Find the actual cost of manufacturing the 51st pair of jeans.
(Round your answer to two decimal places.)
$

Maximizing Profits
The quantity demanded each month of the Walter Serkin recording
of Beethoven's Moonlight Sonata, produced by Phonola Media, is
related to the price per compact disc. The equation p = −0.00042x +
9 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x
is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging x
copies of this classical recording is given...

7. Suppose the cost, in dollars, of producing x items is given
by the function C(x) = 1/6x3+ 2x2+ 30.
Current production is at x = 9 units.
(a) (3 points) Use marginal analysis to find the marginal cost
of producing the 10th unit.
(b) (3 points) Find the actual cost of producing the 10th
unit.

A pen manufacturer determined that the total cost in dollars of
producing x dozen pens in one day is given by C(x) = 350 + 2x -
0.01x2, 0 ≤ x ≤ 100 a. Find the expression for marginal cost. b.
Find the level of output (x) where the marginal cost is minimum. c.
Find the marginal cost at a production level of where the marginal
cost is minimum

The cost in dollars of producing x units of a commodity is:
C(x)= 920 + 2x - .02x2 + .00007x3
a) use the marginal analysis to estimate the cost of the 95th
unit
b) what is the actual cost of the 95th unit?
Please explain in step by step
actual cost : c(x) - c(x) = ? is c(95) - c(94) = correct?
I am getting a different answer
Thank you

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