Question

The monthly demand function for *x* units of a product
sold by a monopoly is

* p* = 6,100 −
1/2

a) Find the profit function, P(x), in dollars.

b) Find the number of units that maximizes profits. (Round your answer to the nearest whole number.)

c) Find the maximum profit. (Round your answer to the nearest cent.)

Answer #1

The monthly demand function for a product sold by a monopoly is
p = 2200 − (1/3)x^2 dollars, and the average cost is C = 1000 + 10x
+ x^2 dollars. Production is limited to 1000 units and x is in
hundreds of units.
(a) Find the quantity (in hundreds of units) that will give
maximum profit.
(b) Find the maximum profit. (Round your answer to the nearest
cent.)

1. In this problem, p and C are in dollars and
x is the number of units.
A monopoly has a total cost function
C = 1000 + 216x + 0x2 for
its product, which has demand function p = 648 ?
3x ? 2x2.
Find the consumer's surplus at the point where the monopoly has
maximum profit. (Round your answer to the nearest cent.)
2. In this problem, p is in dollars and x is
the number of units....

The weekly demand function for x units of a product
sold by only one firm is p = 400 − 1/2x dollars, and the average
cost of production and sale is
C = 100 + 2x dollars.
(a) Find the quantity that will maximize profit.
units
(b) Find the selling price at this optimal quantity.
$ per unit
(c) What is the maximum profit?
$
The weekly demand function for x units of a product sold by only
one firm is...

The weekly demand function for x units of a product
sold by only one firm is
p = 600 −1/2x dollars
,
and the average cost of production and sale is
C = 300 + 2x dollars.
(a) Find the quantity that will maximize profit.
units
(b) Find the selling price at this optimal quantity.
$ per unit
(c) What is the maximum profit?
$

The weekly demand function for x units of a product
sold by only one firm is
p = 300 −
1
2
x dollars,
and the average cost of production and sale is
C = 200 + 2x dollars.
(a) Find the quantity that will maximize profit.
units
(b) Find the selling price at this optimal quantity.
$ per unit
(c) What is the maximum profit?

The weekly demand function for x units of a product sold by only
one firm is p = 800 − 1 /2 x dollars, and the average cost of
production and sale is C = 300 + 2x dollars. (a) Find the quantity
that will maximize profit_____ units
(b) Find the selling price at this optimal quantity. $_____ per
unit
(c) What is the maximum profit?________

If, in a monopoly market, the demand for a product is p
= 120 − 0.80x and the revenue function is R =
px, where x is the number of units sold, what
price will maximize revenue? (Round your answer to the nearest
cent.)

In this problem, p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if
its demand function is p = 100 − x2 and its supply function is p =
x2 + 6x + 44. (Round your answer to the nearest cent.)

The total cost function for a product is
C(x) = 850
ln(x + 10) + 1800
where x is the number of units produced.
(a) Find the total cost of producing 300 units. (Round your
answer to the nearest cent.)
$
(b) Producing how many units will give total costs of $8500? (Round
your answer to the nearest whole number.)
units

Find the maximum profit and the number of units that must be
produced and sold in order to yield the maximum profit. Assume
that revenue, R(x), and cost, C(x), of producing x units are in
dollars.
R(x)=40x−0.1x^2, C(x)=4x+10
In order to yield the maximum profit of $__ , __ units must be
produced and sold.
(Simplify your answers. Round to the nearest cent as
needed.)

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