Question

The marketing department of a business has determined that the
demand for a product can be modeled by **p = 50/x**.
The cost of producing x units is given by **c(x)=
.5x+500**. What price will yield a maximum profit?

Answer #1

The marketing department of a business has determined that the
demand for a product can be modeled by p = 24 √ x , where p is the
price per unit (in dollars) and x is the number of units. The cost
(in dollars) of producing x units is given by C = 0.5x + 500. What
price will yield a maximum profit?

1. A. The Cobb-Douglas production function, f(x,y)=40x^1/4y^3/4,
describes the production of a company for which each unit of labor
costs $100 and each unit of capital costs $125. For a new project,
the company has allocated $60,000 for labor and capital. Find the
amount of money that the company should allocate to labor and
capital to maximize production.
B. The marketing department of a business has determined that
the demand for a product can be modeled by p=(50/(square root of...

Your marketing department has determined that the price you can
expect to sell the appliances for is approximated by the demand
curve p =400e^( –0.0006D) + 75.
Your setup cost to produce up to 10000 appliances per month is
$50,000 and the incremental cost per appliance is $50. Plot profit
as a function of demand and determine the optimal value of
demand.

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.

A commodity has a demand function modeled by p = 103 − 0.5x and
a total cost function modeled by C = 30x + 31.75, where x is the
number of units.
(a) What price yields a maximum profit?
(b) When the profit is maximized, what is the average cost per
unit? (Round your answer to two decimal places.)

2) Product price (p) and demand (D) are typically related
linearly. Company A has performed extensive market research to
develop a better relationship. They determined that the selling
price of a product, p, is related to the demand for their product,
D, in accordance with the following improved relationship
P= 92.5 – 0.09 (D^1.1) (in
dollars)
Demand is given in units per year. In addition, there is a fixed
cost of $40,000 per year and a variable cost of $40...

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...

Revenue
A small business assumes that the demand function for one of its
new products can be modeled by
p =
Cekx.
When p = $40, x = 800 units, and when
p = $30, x = 1500 units.
(a)
Solve for C and k. (Round C to four
decimal places and k to seven decimal places.)
C
=
k
=
(b)
Find the values of x and p that will maximize
the revenue for this product. (Round x to...

The marketing research department of a computer company used a
large city to test market the firm’s new laptop. The department
found that the relationship between price p (dollars per unit) and
the demand x (units per week) was given approximately by
p=1,296-0.12x^2 0≤x≤80) So, weekly revenue can be approximated by
R(x)=xp=1,296x-0.12x^3 Find all critical numbers of the function,
then use the second-derivative test on each critical number to
determine if it is a local maximum or minimum in order...

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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