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.

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) =

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) =

Read more about marginal cost function at; link

a)

b)

c)

Step-by-step explanation:

For total cost function , average cost is given by i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e.,

Given:

Average cost =

a)

At x = 50 units,

b)

Average cost =

c)

Marginal average cost:

Differentiate average cost with respect to

Take

using quotient rule,

Therefore,

b

step-by-step explanation: