Question
In: Math
The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is...
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 991st and the 1971st disc?
b. What is the marginal cost when x = 990 and 1970?
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) = 9,600x − 120x2
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 (in dollars) should the airline charge in order to maximize their revenue?
Solutions
milcah answered 2 years agoRelated Solutions
Compact discs and long-playing records are made from similar materials. The former have a diameter of...
Compact discs and long-playing records are made
from similar materials. The former have a diameter of about 12 cm,
and the latter, about 32 cm. When in use, records spin at 33.333
rev/min, and compact discs spin at, say, 410 rev/min. Ignoring the
holes in both objects and assuming that a compact disc has two
thirds the thickness of a record and 0.90 of its density, what is
the ratio of the angular momentum of a compact disc in use...
A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x...
A manufacturer of tennis rackets finds that the total cost
C(x) (in dollars) of manufacturing x
rackets/day is given by
C(x) = 900 + 3x + 0.0003x2.
Each racket can be sold at a price of p dollars, where
p is related to x by the demand equation
p = 5 − 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 revenue...
If the total cost function for a product is C(x) = 8(x + 5)^3 dollars, where...
If the total cost function for a product is C(x) = 8(x + 5)^3
dollars, where x represents the number of hundreds of units
produced, producing how many units will minimize average cost? x =
hundred units
Find the minimum average cost per hundred units. $
A firm incurred a total fixed cost of $400,000 and total variable cost of $600,000 to...
A firm incurred a total fixed cost of $400,000 and total
variable cost of $600,000 to produce 50,000 units of output.
What are the average fixed cost (AFC), average variable cost
(AVC), and average total cost (ATC)?
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...
The table below shows
the weekly marginal cost (MC) and average total cost (ATC) for
Smitten, a perfectly competitive firm that produces children’s
mittens in a competitive market.
Smitten's
Production Costs
Quantity (pairs of mittens)
Marginal Cost (dollars)
Average Total Cost (dollars)
20
$1.60
$1.25
25
2.00
1.40
30
2.45
1.58
35
3.55
1.86
40
4.00
2.13
45
5.50
2.50
50
6.00
2.85
55
8.50
3.36
Instructions: In part a, enter your answer as a
whole number. In parts b–d,...
8. The table below shows the weekly marginal cost (MC) and average total cost (ATC) for...
8. The table below shows the weekly marginal cost (MC) and
average total cost (ATC) for Buddies, a perfectly competitive firm
that produces novelty ear buds in a competitive market. The market
price of ear buds is $6.00 per pair.
Quantity of Ear buds
MC ($)
ATC ($)
5
-
9
10
2
5.5
15
2.44
4.48
20
3.56
4.25
25
4.5
4.3
30
5.02
4.42
35
5.96
4.64
40
8.56
5.13
Instructions: In part a, enter your answer as...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...
The table below shows the weekly marginal cost (MC) and average
total cost (ATC) for Smitten, a perfectly competitive firm that
produces children’s mittens in a competitive market.
Smitten's Production Costs
Quantity (pairs of mittens)
Marginal Cost (dollars)
Average Total Cost (dollars)
20
$1.60
$1.25
25
2.00
1.40
30
2.45
1.58
35
3.55
1.86
40
4.00
2.13
45
5.50
2.50
50
6.00
2.85
55
8.50
3.36
Instructions: In part a, enter your answer as a
whole number. In parts b–d,...
The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Smitten,...
The table below shows the weekly marginal cost (MC) and average
total cost (ATC) for Smitten, a perfectly competitive firm that
produces children’s mittens in a competitive market.
Smitten's Production Costs
Quantity (pairs of mittens)
Marginal Cost (dollars)
Average Total Cost (dollars)
10
$1.60
$5.00
15
2.00
4.00
20
2.45
3.61
25
3.55
3.60
30
4.00
3.67
35
5.50
3.93
40
6.00
4.19
45
8.50
4.67
Instructions: In part a, enter your answer as a
whole number. In parts b–d,...
1)The total profit P(x) (in thousands of dollars) from a sale of x thousand units of...
1)The total profit P(x) (in thousands of dollars) from a sale
of x thousand units of a new product is given by
P(x)= ln (-x3+9x2+48x+1) (0≤x≤10).
a) Find the number of units that should be sold in order to
maximize the total profit.
b) What is the maximum profit?
2)Suppose that the cost function for a product is given by
C(x)=0.003x3+9x+9,610.
Find the production level (i.e., value of x) that will produce
the minimum average cost per unit C(x).
a)The...
The cafeteria at X Company incurred the following costs in September: Cost Item Cost Supervisor salary...
The cafeteria at X Company incurred the following costs in
September: Cost Item Cost Supervisor salary $5,920 Hourly workers
wages 32,088 Food 11,074 Equipment 6,810 Supplies 3,118 Total
$59,010 The hourly workers wages, food costs, and supplies costs
were variable; the supervisor salary and equipment costs were
fixed. The cafeteria served 13,000 meals during September. In
October, the cafeteria is expected to serve 12,350 meals. Using
account analysis with this data, estimate the total cafeteria cost
in October [round variable...
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