Question

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*) = 48*x*

and that the total cost function is given by

* C*(

(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 |*MP*(100)| dollars. At *x* = 100,
*MP*(100) predicts that profit will decrease by
|*MP*(100)| dollars. At *x* =
100, *MP*(100) predicts that cost will decrease by
|*MP*(100)| dollars. At *x* = 100, *MP*(100)
predicts that profit will increase by |*MP*(100)|
dollars.

(d) Find *P*(101) − *P*(100).

$

Explain what this value represents.

The sale of the 100th unit will increase profit by
|*P*(101) − *P*(100)| dollars. The sale of the 101st
unit will increase profit by |*P*(101) − *P*(100)|
dollars. The sale of the 100th unit will
decrease profit by |*P*(101) − *P*(100)| dollars. The
sale of the 101st unit will decrease profit by |*P*(101) −
*P*(100)| dollars.

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...

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...

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. 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...

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...

Consider that for ‘x’ units
sold, the total REVENUE function is : R(x) =
75x2– 15x
– 200 and the total COST function is :
C(x) = 750 + 25x –
100 √ x.
(b)
Also determine values of (i) Marginal Revenue when x= 25
and (ii) MP(25), where marginal Revenue is
defined as derivative of Revenue function and MP(x) =
P'(x).

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.

The cost function C and the price-demand function
p are given. Assume that the value of
C(x)
and
p(x)
are in dollars. Complete the following.
C(x) =
x2
100
+ 7x + 3000;
p(x) = −
x
40
+ 5
(a) Determine the revenue function R and the profit
function P.
R(x)
=
P(x)
=
(b) Determine the marginal cost function MC and the
marginal profit function MP.
MC(x)
=
MP(x)
=
Here is a picture of the problem:
https://gyazo.com/b194ec1a9b7787b8b81ad12388ff915e

The total cost and the total revenue (in dollars) for the
production and sale of x ski jackets are given by
C(x)=26x+20,440
and
R(x)=200x-.2x^2 for 0
(A)
Find the value of x where the graph of R(x) has a horizontal
tangent line.
(B)
Find the profit function P(x).
(C)
Find the value of x where the graph of P(x) has a horizontal
tangent line.
(D)
Graph C(x), R(x), and P(x) on the same coordinate system for
0less than or equals≤xless...

A manufacturer has determined that the revenue from the sale of
tiles is given by R(x) = 34x – 0.03x2 dollars. The cost
of producing x tiles in C(x) = 10,500 + 55x dollars. Find the
profit function and any break-even points? Find P(200), P(400), and
P(600)? Find the marginal profit function, P¢(x)? Find P¢(200),
P¢(400), P¢(600)? draw the graph of P(x) and P¢(x) and explain both
graphs.

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