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kkurt [141]
3 years ago
5

A firm has a revenue function that can be represented by r (x)=700x-0.35x^2, where r (x) is the total revenue (in dollars) and x

is the number of units sold. How many units need to be sold to produce the maximum revenue? How many in dollars is the maximum revenue when the maximum of units are sold?
Mathematics
1 answer:
Fudgin [204]3 years ago
5 0

Answer:

How many units need to be sold to produce the maximum revenue? 1000 units

How many in dollars is the maximum revenue when the maximum of units are sold? $350,000

Step-by-step explanation:

We get max value of a function if we differentiate it and set it equal to 0.

We need to differentiate r(x) and set it equal to 0 and solve for x.

<u><em>That would be number of units sold to get max revenue.</em></u>

<u><em /></u>

<u>Then we take that "x" value and substitute into r(x) to get the max revenue amount.</u>

<u />

Before differentiating, we see the rules shown below:

f(x)=ax^n\\f'(x)=n*ax^{n-1}

Where

f'(x) is the differentiated function

Now, let's do the process:

r (x)=700x-0.35x^2\\r(x)=700-2*0.35x\\r(x)=700-0.7x\\0=700-0.7x\\0.7x=700\\x=1000

So, 1000 units need to be sold for max revenue

Now, substituting, we get:

r (x)=700x-0.35x^2\\r(1000)=700(1000)-0.35(1000)^2\\r(1000)=350,000

The max revenue amount is $350,000

You might be interested in
Write in slope intercept form an equation of the line that passes through (-2,5),(-1,1)
Juliette [100K]

Answer:

y=-4x-3

Step-by-step explanation:

Hi there!

We are given the following two points: (-2,5) and (-1,1)

We want to write the equation of the line that passes through these two lines in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope

The formula for the slope (m) calculated from 2 points is \frac{y_2-y_1}{x_2-x_1}, where (x_1, y_1) and (x_2, y_2) are points

We have everything we need to calculate the slope, but let's label the value of the points to avoid any confusion

x_1=-2\\y_1=5\\x_2=-1\\y_2=1

Now substitute into the formula

m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{1-5}{-1--2}
Simplify

m=\frac{1-5}{-1+2}

Subtract

m=\frac{-4}{1}

Divide

m=-4

Now substitute -4 as m into the equation:

y=-4x+b

Now we need to find b

As the equation passes through both (-2, 5) and (-1, 1), we can use either point to help solve for b.

Taking (-2,5) for example:

Substitute -2 as x and 5 as y:

5=-4(-2)+b

Multiply

5=8+b

Subtract 8 from both sides

-3=b

Substitute -3 as b.

y=-4x-3

Hope this helps!

See more on this topic here: brainly.com/question/27304092

4 0
2 years ago
Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v
k0ka [10]

I'll use subscript notation for brevity, i.e. \frac{\partial f}{\partial x}=f_x.

By the chain rule,

z_u=z_xx_u+z_yy_u

z_v=z_xx_v+z_yy_v

z_w=z_xx_w+z_yy_w

We have

z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}

and

\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}

When u=1,v=1,w=0, we have

\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}

and the partial derivatives take on values of

\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}

So we end up with

\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}

3 0
3 years ago
Pls help, thanks for the answer thanks
siniylev [52]
A. Length: 7, Width: 5
B. Perimeter: 24
C. Area: 35
4 0
3 years ago
Please help with explanation if you can
sertanlavr [38]

Answer:

Step-by-step explanation:

The answer is b

8 0
2 years ago
Read 2 more answers
What is the quotient and the remainder of 7 divided by 5839
eduard

Answer: 834.142857143

Step-by-step explanation: I did it on paper this is like 3rd grade math.

4 0
2 years ago
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