Mathematics, 10.02.2020 22:52 Reddev

The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for each of the following production. a) 50 unitsb) x unitsc) find the marginal average cost function.

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Answer from: sofia3226

1) The average cost for the production at 50 units and x units respectively are;

A) A(50) = 74/10025

B) A(x) = (3x - 2)/(8x² + x)

2) The marginal average cost function is; M(x) = $\frac{-24x^{2} + 32x + 2}{x^{2}(8x^{2} + 1)^{2} }$

We are given Total cost function as;

C(x) = (3x - 2)/(8x + 1)

The formula for the average cost is;

A(x) = (C(x))/x

where x is the units of the product

Thus;

A) At x = 50 units;

A(50) = [(3(50) - 2)/(8(50) + 1)]/50

A(50) = (148/401)/50

A(50) = 74/10025

B) At x units;

A(x) = [(3x - 2)/(8x + 1)]/x

A(x) = (3x - 2)/[x(8x + 1)]

A(x) = (3x - 2)/(8x² + x)

C) Formula for average marginal cost function is;

M(x) = [(C(x))/x]'

(C(x))/x = (3x - 2)/(8x² + x)

Thus;

M(x) = ['(3x - 2)/(8x² + x)]'

From online differentiation calculator, we have;

M(x) = $\frac{-24x^{2} + 32x + 2}{x^{2}(8x^{2} + 1)^{2} }$

Read more about marginal cost function at; link

Answer from: christeinberg1

a) $\frac{74}{10025}$

b) $\frac{3x-2}{x(8x+1)}$

c) $\frac{-24x^2+32x-2}{(8x^2+x)^2}$

Step-by-step explanation:

For total cost function c(x) , average cost is given by $\frac{c(x)}{x}$ i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., $\left ( \frac{c(x)}{x} \right )'$

Given: $c(x)=\frac{3x-2}{8x+1}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

At x = 50 units,

$\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

Marginal average cost:

Differentiate average cost with respect to

Take $f=3x-2\,,\,g=8x^2+x$

using quotient rule, $\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}$

Therefore,

$\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}$

Answer from: Quest

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What are the y-intercept and the slope of the line represented in the graph? a. y-intercept = -4 and

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is