Question

A manufacturing company of a certain product has a fixed cost of $40 and a variable cost of 2x^3+13x, what is the total cost function and the cost to produce 50 of these products? What is the marginal cost when x = 50?

At what level of output will average cost per unit be a minimum? What is this minimum?

If the demand price for this product is set
at *d(x) = -x^2+49,* determine the amount of production
which will maximize the
profit.

Determine the price at which maximum profit occurs and calculate the maximum profit.

Answer #1

The marginal cost of a product can be thought of as the cost of
producing one additional unit of output. For example, if the
marginal cost of producing the 50th product is $6.20, it cost
$6.20 to increase production from 49 to 50 units of output. Suppose
the marginal cost C (in dollars) to produce x thousand mp3 players
is given by the function Upper C left parenthesis x right
parenthesis equals x squared minus 120 x plus 7500.C(x) =...

The revenue function of a company is given by
R(x)=-2x^2+25x+150, the cost function is given by C(x)=13x+100
a. Find the marginal cost and marginal revenue function.
b. Find the production level x where the profit is maximized.
Then find the maximum profit.

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...

Assume the production cost (dollars/unit) for a manufacturing
unit of a certain product is given by f (x) = 2(1+x) e-x
+ 5x +250 , where x is the number of units.
Show that the marginal cost of the production will be increased
to a certain value of x, and then decreasing from there on. You can
consider x a continuous variable. For instance, it is alright to
have x=0.1, partial unit of the product. In a practical
application, you...

The demand equation and average cost function of a manufacturing
firm are given by 200 = p+4q and AC = 0.8q^2 + 4 + (25/q)
respectively, where q is the number of units produced. Using the
information provided above, please answer the following questions
(a) Determine the amount of profit when it is maximized. (b)
Determine the amount of average cost at which maximum profit
occurs. (c) Determine the marginal cost of the product when profit
is maximized? (d) Given...

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.

Suppose a company has fixed costs of $53,200 and variable cost
per unit of 2 5 x + 444 dollars, where x is the total number of
units produced. Suppose further that the selling price of its
product is 2372 − 3 5 x dollars per unit. (a) Find the break-even
points. (Enter your answers as a comma-separated list.) x = (b)
Find the maximum revenue. (Round your answer to the nearest cent.)
$ (c) Form the profit function P(x)...

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?
$

Suppose a product has a marginal revenue MR=150 and a marginal
cost MC=x+40, with a fixed cost of $500. How many units will give
you a maximum profit and what is the maximum profit?

Suppose a company has fixed costs of $48,000 and variable cost
per unit of
2/5x + 444 dollars,
where x is the total number of units produced. Suppose
further that the selling price of its product is
2468 −3/5x dollars per unit.
(a) Find the break-even points. (Enter your answers as a
comma-separated list.)
x =
(b) Find the maximum revenue. (Round your answer to the nearest
cent.)
$
(c) Form the profit function P(x) from the cost
and...

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