Question

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

Answer #1

Maximizing Profits
A manufacturer of tennis rackets finds that the total cost
C(x) (in dollars) of manufacturing x
rackets/day is given by
C(x) = 500 + 7x + 0.0003x2.
Each racket can be sold at a price of p dollars, where
p is related to x by the demand equation
p = 10 − 0.0002x.
If all rackets that are manufactured can be sold, find the daily
level of production that will yield a maximum profit for the
manufacturer. Hint:...

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 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?

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.

Marginal Cost
A division of Ditton Industries manufactures a deluxe toaster
oven. Management has determined that the daily marginal cost
function associated with producing these toaster ovens is given
by
C'(x) =
0.0006x2 − 0.14x +
23
where C'(x) is measured in dollars per unit
and x denotes the number of units produced. Management has
also determined that the daily fixed cost incurred in the
production is $700.
(a) Find the total cost incurred by Ditton in producing the
first...

Marginal Cost
A division of Ditton Industries manufactures a deluxe toaster
oven. Management has determined that the daily marginal cost
function associated with producing these toaster ovens is given
by
C'(x) =
0.0006x2 − 0.14x +
25
where C'(x) is measured in dollars per unit
and x denotes the number of units produced. Management has
also determined that the daily fixed cost incurred in the
production is $900.
(a)
Find the total cost incurred by Ditton in producing the first...

Minimizing Average Cost
The total monthly cost (in dollars) incurred by a certain guitar
manufacturer in manufacturing x units of its Professional
Series guitars is given by the function
C(x) = 0.001x2 + 110x + 2250.
(a)
Find the average cost function
C.
C =
(b)
Determine the production level that will result in the smallest
average production cost.
x =

Suppose that the average cost, in dollars, of producing a
shipment of a certain product is
C(x) = 4,000x +
36,000
x
, x > 0
where x is the number of machines used in the
production process.
(a)
Find
C'(x).
C'(x) =
Given the domain of
x > 0,
find the critical value of
C(x).
x =
The critical value is a ---Select--- relative minimum
relative maximum .
(b)
Over what interval does the average cost decrease? (Enter your
answer using...

A manufacturer has determined that the revenue from the sale of
tiles is given by R(x) = 34x – 0.03x2 dollars. The cost
of producing x tiles in C(x) = 10,500 + 55x dollars. Find the
profit function and any break-even points? Find P(200), P(400), and
P(600)? Find the marginal profit function, P¢(x)? Find P¢(200),
P¢(400), P¢(600)? draw the graph of P(x) and P¢(x) and explain both
graphs.

The marginal cost of a product can be thought of as the cost of
producing one additional unit of output. For example, if the
marginal cost of producing the 50th product is $6.20, it cost
$6.20 to increase production from 49 to 50 units of output. Suppose
the marginal cost C (in dollars) to produce x thousand mp3 players
is given by the function Upper C left parenthesis x right
parenthesis equals x squared minus 120 x plus 7500.C(x) =...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 17 minutes ago

asked 27 minutes ago

asked 35 minutes ago

asked 44 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago