Question

1. t

To get full credit for this question make sure you verify that
your answer is indeed the absolute maximum.

Country Motorbikes Incorporated finds that it costs $200 to produce
each motorbike, and that fixed costs are $1500 per day. The price
function is

* p*(

where *p* is the price (in dollars) at which exactly
*x* motorbikes will be sold. Find the quantity Country
Motorbikes should produce and the price it should charge to
maximize profit. Also find the maximum profit.

quantity | motorbikes | |

price | $ | |

profit | $ |

If, and only if, you can't figure out how to set up the
optimization problem above, you may do the problem below for lesser
credit.

Extreme Bicycles' total cost of producing *x* bicycles
is

* C* = 200 + 1300

dollars and its total revenue function is

* R* = 1400

dollars, how many units, *x*, should it produce to
maximize its profit?

*x* = units

Find the maximum profit.

$

Answer #1

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?

Silver Scooter Inc. finds that it costs $300 to produce each
motorized scooter and that the fixed costs are $1,000. The price is
given by p=800?x, where p is the price in dollars at which exactly
x scooters will be sold. Find the quantity of scooters that the
company should produce and the price it should charge to maximize
profit. 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...

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.

silver scooter inc. finds that it costs$ 100 to produce each
motorized scooter and that the fixed costs are $750. the price is
given byp equals 600 minus x commap=600−x, where p is the price in
dollars at which exactly x scooters will be sold. find the quantity
of scooters that the company should produce and the price it should
charge to maximize profit. find 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...

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 = 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?________

retired potter can produce pitchers at a cost of $5 each. He
estimates his price function to be
p = 19 − 0.5x,
where p is the price at which exactly x
pitchers will be sold per week. Find the number of pitchers that he
should produce and the price that he should charge in order to
maximize profit. Also find the maximum profit.
quantity
pitchers
price
$
profit
$

Please answer part 1.
The market for fabric has only one producer. Assume that daily
market demand for fabric is y = 100,000 - 100p, where y denotes the
quantity and p denotes the unit price. Also assume that producing y
units of fabric costs 100y.
1. How many units of fabric should the producer produce and sell
in order to maximize profits? Calculate the profit-maximizing price
and the profit.
2. Now suppose that to produce one unit of fabric...

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