Question

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.)

Answer #1

The monthly demand function for x units of a product
sold by a monopoly is
p = 6,100 −
1/2x2 and its average cost
is C = 3,030 + 2x dollars. Production is
limited to 100 units.
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.)

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 = 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?________

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?
$

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....

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.)

If, in a monopoly market, the demand function for a product is p
= 145 − 0.80x and the revenue function is R = px, where x is the
number of units sold and p is the price per unit, what price will
maximize revenue?

1. Suppose you’re given the following: a) the demand equation p
for a product, which is the price in dollars, and x is the quantity
demanded b) C(x), which is the cost function to produce that
product c) x ranges from 0 to n units
Q. Describe briefly how you would maximize the profit function
P(x), the level of production that will yield a maximum profit for
this manufacturer.

The demand function for a monopolist's product is
p=1300-7q and the average cost per unit for producing q
units is
c=0.004q2-1.6q+100+5000/q
-Find the quantity that minimizes the average cost function and
the corresponding price. Interpret your results.
-What are the quantity and the price that maximize the profit?
What is the maximum profit? Interpret your result.

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