Question

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 p = 400 − 1 2 x 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? $

Answer #1

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?________

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 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.)

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.

Cost, revenue, and profit are in dollars and x is the number of
units. A firm knows that its marginal cost for a product is MC = 3x
+ 30, that its marginal revenue is MR = 70 − 5x, and that the cost
of production of 60 units is $7,380. (a) Find the optimal level of
production. units (b) Find the profit function. P(x) = (c) Find the
profit or loss at the optimal level. There is a of...

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 weekly demand for DVDs manufactured by a certain media
corporation is given by
p = −0.0004x2 + 70
where p denotes the unit price in dollars and
x denotes the quantity demanded. The weekly total cost
function associated with producing these discs is given by
C(x) = −0.001x2 + 19x + 4000
where C(x) denotes the total cost (in dollars)
incurred in pressing x discs. Find the production level
that will yield a maximum profit for the manufacturer.
Hint:...

Suppose that the price p (in dollars) of a product is given by
the demand function p = (18,000 − 60x) / (400 − x) where x
represents the quantity demanded and x < 300. f the daily demand
is decreasing at a rate of 100 units per day, at what rate (in
dollars per day) is the price changing when the price per unit is
$30?

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