Question

Total revenue is in dollars and *x* is the number of
units.

Suppose that the total revenue function for a commodity is

* R* = 81

(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 by about this amount when the number of units is increased from 100 to 101.

(b) Find the marginal revenue function.

*MR* =

(c) Find the marginal revenue (in dollars per unit) at

* x* = 100.

$ per unit

Tell what it predicts about the sale of the next unit and the next
3 units.

The sale of the next unit will ---Select---increasedecrease the revenue by about $ . The sale of the next 3 units will ---Select---increasedecrease the revenue by about $ .

(d) Find

* R*(101) −

$

Explain what this value represents.

actual revenue from 100 units actual revenue from the 101st
unit actual revenue from 101 units actual
revenue from the 100th unit marginal revenue at *x* =
100

Answer #1

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...

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...

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...

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...

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.

Cost, revenue, and profit are in dollars and x is the number of
units. A firm knows that its marginal cost for a product is MC = 3x
+ 30, that its marginal revenue is MR = 70 − 5x, and that the cost
of production of 60 units is $7,380. (a) Find the optimal level of
production. units (b) Find the profit function. P(x) = (c) Find the
profit or loss at the optimal level. There is a of...

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...

1. The revenue (in thousands of dollars) from producing x units
of an item is given by the equation
R(x)=10x-0.002x^2.
Find the average rate of change of revenue when production is
increased from 1200 to 1201 units. Find the instantaneous rate of
change of revenue when 1200 units are produced. Both of these
answers should include units. Explain the difference between these
two values.

Suppose that it costs C(x)=1.30 x2+100.00 x+570.00 dollars to
produce x text books, and that a price per unit of
p(x)=−2.35 x+190.00 is needed to sell all x units.
a) Find the revenue function.
R(x)=
b) Find the profit function.
P(x)=
c) Find the exact cost of producing the 8-th text book.
Exact Cost = dollars.
d) Find the marginal profit if x=7.
Marginal Profit = dollars per unit.

Suppose that it costs c(x) = 156.66x^2 + 13315.79x + 50600.00
dollars to produce (x) boats and that a price per unit of p(x) =
-266.32x + 25300.00 is needed to sell all x units.
a.) Find the revenue function R(x) =
b.) Find the profit function P(x) =
c.) Find the exact cost on the 11th boat exact cost =
d.) Find the marginal profit if x=10
Marginal profit =

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