Question

Suppose that the total revenue in dollars from the sales of x hundred televisions is given by

R(x)=-100(x^2-16x)

a) Find the marginal revenue function

b) Find R[Prime](9)

c) If the manufacturer wants to maximize revenue , should he make more or less than 900 televisions? Why?

d) What does R[prime](9) mean and what does it predict? Compare this with actual total revenue.

Answer #1

Total revenue is in dollars and x is the number of
units.
Suppose that the total revenue function for a commodity is
R = 81x −
0.02x2.
(a) Find R(100).
$
Tell what it represents.
The actual revenue of the 100th unit is this amount. The revenue
decreases by about this amount when the number of units is
increased from 100 to 101. 100 units
produce this amount of revenue. 101 units produce this amount of
revenue. The revenue increases...

Total revenue is in dollars and x is the number of
units.
Suppose that in a monopoly market, the demand function for a
product is given by
p = 450 − 0.1x
where x is the number of units and p is the
price in dollars.
(a) Find the total revenue from the sale of 500 units.
$
(b) Find the marginal revenue MR at 500 units.
MR = $
Interpret this value.
The 501st unit will lose |MR| dollars...

The marginal revenue of a company is given by
r(x)=x^3-0.3x^2+0.1 and the marginal cost is given by
c(x)=x\sqrt{-x^2+100} both measured in thousands of dollars per
hundred units (x) produced. Find the total profit for x=1 to x=4
hundred units produced.

The total profit Upper P(x) (in thousands of dollars) from the
sale of x hundred thousand pillows is approximated by:
P(x) = -x^3 + 9x^2 + 165x - 200 , x ≥ 5
Find the number of hundred thousands of pillows that must be
sold to maximize profit. Find the maximum profit.

Cost, revenue, and profit are in dollars and x is the
number of units.
Suppose that the total revenue function is given by
R(x) = 48x
and that the total cost function is given by
C(x) = 70 +
29x + 0.1x2.
(a) Find P(100).
P(100) =
(b) Find the marginal profit function MP.
MP =
(c) Find MP at x = 100.
MP(100) =
Explain what it predicts.
At x = 100, MP(100) predicts that cost will
increase by...

A company estimates that the revenue (in dollars) from the sale
of x doghouses is given by the function. Approximate the change in
revenue if sales go from 90 to 100.
R(x) = 12000 ln(0.02x+1)

Total revenue is in dollars and x is the number of units.
Suppose that in a monopoly market, the demand function for a
product is given by the following equation, where x is the number
of units and p is the price in dollars. p = 370 − 0.3x (a) Find the
total revenue from the sale of 500 units. $ (b) Find the marginal
revenue at 500 units. $ (c) Is more revenue expected from the 501st
unit sold...

Cost, revenue, and profit are in dollars and x is the
number of units.
Suppose that the total revenue function for a product is
R(x) =
55x
and that the total cost function is
C(x) = 2200 +
35x + 0.01x2.
(a) Find the profit from the production and sale of 500
units.
(b) Find the marginal profit function
(c) Find MP at x = 500.
Explain what it predicts.
The total profit will ------ by approximately $------- on the...

The revenue R (in dollars) from renting x apartments can be
modeled by R = 2x(500 + 36x − x2). (a) Find the marginal revenue,
in dollars, when x = 14. $ (b) Find the additional revenue, in
dollars, when the number of rentals is increased from 14 to 15. $
Correct: Your answer is correct. (c) Compare the results of parts
(a) and (b).The revenue R (in dollars) from renting
x apartments can be modeled by
R = 2x(500...

The total revenue function for a certain product is given by
R=590x dollars, and the total cost function for this product
is
C=15,000 +50x + x squared 2 dollars, where x is the number of
units of the product that are produced and sold.
a.
Find the profit function.
b.
Find the number of units that gives maximum profit.
c.
Find the maximum possible profit.

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