Question

**Marginal Revenue for Producing Loudspeakers**

The management of Acrosonic plans to market the ElectroStat, an
electrostatic speaker system. The marketing department has
determined that the demand for these speakers is represented by the
following function, where *p* denotes the speaker's unit
price (in dollars) and *x* denotes the quantity demanded.
Find the following functions (in dollars), find the value (in
dollars) and interpret your results.

*p* = −0.01*x* +
700 (0 ≤ *x* ≤
20,000)

(a)

Find the revenue function *R*.

*R*(*x*) =

(b)

Find the marginal revenue function *R'*(*x*).

*R'*(*x*) =

(c)

Compute the following value.

*R'*(3,300) =

Interpret your results.

When the level of production is units, the production of the next speaker system will bring an additional revenue of dollars.

Answer #1

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...

The management of a watch company has determined that the daily
marginal revenue function associated with producing and selling
their travel clocks is given by:
R ′ (x) = - 0.08x + 24, where x denotes the number of units
produced and sold and R ′ (x) is measured in dollars/unit.
a) Use the Marginal revenue function to estimate the revenue from
the sale of the 200th clock. Round your answer down to the nearest
penny.
b) Determine the...

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) = 6,000x −
100x2
(a)
Find the marginal revenue R'(x).
R'(x) =
(b)
Compute the following values.
R'(29)
=
R'(30)
=
R'(31)
=
(c)
Based on the results of part (b), what price (in dollars) should
the airline charge in order to maximize their revenue?
$

Total revenue is in dollars and x is the number of
units.
Suppose that in a monopoly market, the demand function for a
product is given by
p = 450 − 0.1x
where x is the number of units and p is the
price in dollars.
(a) Find the total revenue from the sale of 500 units.
$
(b) Find the marginal revenue MR at 500 units.
MR = $
Interpret this value.
The 501st unit will lose |MR| dollars...

Total revenue is in dollars and x is the number of units.
Suppose that in a monopoly market, the demand function for a
product is given by the following equation, where x is the number
of units and p is the price in dollars. p = 370 − 0.3x (a) Find the
total revenue from the sale of 500 units. $ (b) Find the marginal
revenue at 500 units. $ (c) Is more revenue expected from the 501st
unit sold...

Marginal Revenue for an Apartment Complex
Lynbrook West, an apartment complex, has 100 two-bedroom units.
The monthly profit (in dollars) realized from renting x
apartments is represented by the following function.
P(x) = -9x2 +
1520x - 52000
(a)
What is the actual profit realized from renting the 41st unit,
assuming that 40 units have already been rented?
$
(b)
Compute the marginal profit when x = 40 and compare
your results with that obtained in part (a).
$

Write a word story for this problem
If total revenue received from the sale of x items is given by
R(x) =10ln(3x+1) while the total cost to produce x items is C(X)
=X/3
find the following.
(a) The marginal revenue
(b) The profit function P(x)
(c) The marginal profit when
X=30
(d) Interpret the results of part (c).

Pulsar manufactures a series of 20-in. flat-tube LCD
televisions. The quantity x of these sets demanded each
week is related to the wholesale unit price p by the
equation
p = −0.059x + 290
The weekly total cost incurred by Pulsar for producing
x sets is
C(x) = 0.000006x3 -
0.07x2 + 410x + 69000.
(a) Find the revenue function R.
R(x) =
Find the profit function P.
P(x) =
.011x2−120x−0.000006x3−69000
(b) Find the marginal cost function C '....

7. A furniture company is faced with the following the
price-demand function, revenue function, and cost function:
p(x) = 90 - 5x
R(x) = xp(x)
C(x) = 250 + 15x
where p(x) is the price in dollars at which x hundred chairs can be
sold and R(x) and C(x) are in thousands of dollars.
(a) Give the revenue R for producing 1200 chairs.
(b) Find the production level that gives the break-even
point.
(c) Find the production level that gives...

Cost, revenue, and profit are in dollars and x is the
number of units.
Suppose that the total revenue function for a product is
R(x) =
55x
and that the total cost function is
C(x) = 2200 +
35x + 0.01x2.
(a) Find the profit from the production and sale of 500
units.
(b) Find the marginal profit function
(c) Find MP at x = 500.
Explain what it predicts.
The total profit will ------ by approximately $------- on the...

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