Question

A company making widgets has a price-demand equation p(x) = 400 − .02x where x is the monthly demand and p is the price per widget and the cost equation is C(x) = 200x + 20, 000. Find the price that maximizes the profit and give the maximum profit.

Answer #1

a) The Cost of selling widgets is given by the cost function
c(x)= 4x+10.
The price of each widget is given by the function p=
50-0.05x.
A) How many widgets must be sold to maximize profit?
B) What will be the Maximum Profit?
C) What price per widget must be charged in order to maximize
profit.

A). A company produces widgets: it is called widget
incorporated. The widgets are produced at a constant marginal and
average cost of 100 coins per widget. The market demand is
Q=80-0.2P.
What is the equilibrium price if Widget Incorporated produces as
a single price monopolist?
Suppose the state adds a 20 coin tax per widget on the
production of widgets. How much revenue will the tax raise? How
much surplus value will be lost? How much profit will Widget
Incorporated...

A company produces x widgets for a cost of C(x) dollars and
sells them for 2280 dollars per widget.
If the cost function is C(x)=6450+760x+0.8x2, find the production
level that will maximize profit.
x = _____widgets
Be sure to apply a test to check that you have found the
maximum.

The demand equation for widgets is P=20-2QD, where P is the
price of cookies in dollars and QD is the quantity demanded.
Calculate the price elasticity of demand for cookies between
QD1=2 and QD2=3.
Scalpers sell their tickets outside of theatres, sporting
events and concerts. Demand for scalper tickets is usually quite
high for sold-out events, as consumers have no other alternative if
they want to purchase tickets.
Using demand and
supply curves, show the change in equilibrium price and...

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...

1) For a company the demand equation is given by p = 100 -
0.025x, where p represents the price per unit when x quantity of
units is sold. Determine the marginal revenue when 2,500 units are
sold, that is, R ’(2,500) and interpret the result.
2) The total weekly cost in dollars for manufacturing x
calculators in a company is given by the function C (x) = 10x +
2,500. Determine the marginal average cost function.

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.)

Find the price that will maximize profit for the demand and cost
functions, where p is the price, x is the number
of units, and C is the cost.
Demand Function
Cost Function
p = 78 − 0.1 Sqared Root (x)***
x
***
C = 33x + 550
$ ______per unit

Find the consumers' surplus at a price level of $7 for the
price-demand equation p=D(x)=35−0.2x where p is the price and x is
the demand. Do not include a dollar sign or any commas in your
answer.

If a price-demand equation is solved for p, then price is
expressed as p=g(x) and x becomes the independent variable. In this
case, it can be shown that the elasticity of demand is given by
E(x)= -g(x)/xg'(x) . Use the given price-demand equation to find
the values of x for which demand is elastic and for which demand is
inelastic. p=g(x)=9000-0.1x^2

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