Question

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.

Answer #1

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...

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 = 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 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:...

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 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.)

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?

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.

The demand for a product is given by p = d ( q ) = − 0.8 q + 150
and the supply for the same product is given by p = s ( q ) = 5.2
q. For both functions, q is the quantity and p is
the price in dollars. Suppose the price is set artificially at $70
(which is below the equilibrium price).
a) Find the quantity supplied and the quantity demanded at this
price.
b)...

The short term demand for a product can be approximated by
q=D(p)=175(100−p2) where p represents the price of the product, in
dollars, and q is the quantity demanded. (a) Determine the
elasticity function. E(p)= _______ equation editorEquation Editor
(b) Use the elasticity of demand to find the price which maximizes
revenue for this product p= ______ equation editorEquation Editor
dollars. Round to two decimal places.

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