Question

1 point) The price-demand and cost functions for the production of microwaves are given as

p=280−x40p=280−x40

and

C(x)=20000+100x,C(x)=20000+100x,

where xx is the number of microwaves that can be sold at a price
of pp dollars per unit and C(x)C(x) is the total cost (in dollars)
of producing xx units.

(A) Find the marginal cost as a function of xx.

C′(x)C′(x) =

(B) Find the revenue function in terms of xx.

R(x)R(x) =

(C) Find the marginal revenue function in terms of xx.

R′(x)R′(x) =

(D) Evaluate the marginal revenue function at x=1500x=1500.

R′(1500)R′(1500) =

(E) Find the profit function in terms of xx.

P(x)P(x) =

(F) Evaluate the marginal profit function at x=1500x=1500.

P′(1500)P′(1500) =

Answer #1

The price-demand equation and the cost function for the
production of 4K Tv’s are given respectively. x = 9000 − 30p and
c(x) = 150000 + 30x Where x is the number of 4k TV’s that can be
sold at a price p and c(x) is the total cost in dollars in
producing x Tv’s.
a) Express the price p as a function of demand x, and find the
domain of this function.
b) Find the marginal cost function
c)...

* City Computers has determined that the price-demand and
revenue functions are given by p(x) = 2,000 – 6x and
R(x) = x(2,000 – 6x), where x is in thousands of computers.
This means that R(x) is measured in thousands of dollars.
Additionally we know:
* The fixed cost is $100,000.
* The variable cost is $250 per computer.
This means that the cost function is given by C(x) = 100 +
250x. Also again C(x) is measured in thousands...

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

7. A furniture company is faced with the following the
price-demand function, revenue function, and cost function:
p(x) = 90 - 5x
R(x) = xp(x)
C(x) = 250 + 15x
where p(x) is the price in dollars at which x hundred chairs can be
sold and R(x) and C(x) are in thousands of dollars.
(a) Give the revenue R for producing 1200 chairs.
(b) Find the production level that gives the break-even
point.
(c) Find the production level that gives...

1. 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) = x^2/100 + 6x + 1000; p(x) = x/20+25
(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)
=
3. Determine the derivative for the given single-term function.
When appropriate,...

total revenue and total cost functions for the production and
sale of xTV's are given as
R(x)=130x−0.7x2
and
C(x)=3950+21x.
(A) Find the value of x where the graph of R(x)R(x) has a
horizontal tangent line. xvalues is
equation editor
Equation Editor
(B) Find the profit function in terms of x.
P(x)=
equation editor
Equation Editor
(C) Find the value of xx where the graph of P(x) has a horizontal
tangent line.
x values =
equation editor
Equation Editor
(D) List...

1) Suppose the cost in dollars of manufacturing q item is given
by: C= 2000q + 3500
and the demand equation is given by: q= sqrt(15,000-1.5p)
in terms of the demand q,
a) find an expression for the revenue R
b) find an expression for the profit P
c) find an expression for the marginal profit
d) Determine the value of the marginal profit when the price is
$5000
2) A manufacturer sells video games with the following cost and...

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

Acrosonic's production department estimates that the total cost
(in dollars) incurred in manufacturing x ElectroStat
speaker systems in the first year of production will be represented
by the following function, where R(x) is the
revenue function in dollars and x denotes the quantity
demanded. Find the following functions (in dollars) and compute the
values (in dollars).
C(x) = 110x +
27,000 and R(x)
= −0.04x2 + 800x
(a)Find the profit function P.
(b)Find the marginal profit function P '.
(c)Compute the following...

1). Find the consumer and producer surpluses by using the demand
and supply functions, where p is the price (in dollars)
and x is the number of units (in millions).
Demand Function
Supply Function
p = 410 − x
p = 160 + x
consumer surplus $_________
millionsproducer surplus $ ________millions
2) Find the consumer and producer surpluses by using the demand
and supply functions, where p is the price (in dollars)
and x is the number of units (in...

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