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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Cost If the marginal cost function for x units of a product is M C ¯  = 1 + 3 In  ( x  + 1 ) dollars per unit and if the fixed cost is $100, find the total cost function.

To determine

To calculate: The total cost function if marginal cost for x units of a product is MC¯=1+3ln(x+1) dollars per unit and the fixed cost is $100.

Explanation

Given Information:

Marginal cost for x units of a good is MC¯=1+3ln(x+1) and the fixed cost is $100.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

As it is provided the marginal cost for x units of a good is,

MC¯=1+3ln(x+1)

Now, to obtain the total cost function, integrate the marginal cost function as the marginal cost function is the derivative of total cost function, so,

C(x)=(1+3ln(x+1))dx

Now, use the method of integration by parts by splitting the integrands into two components, thus,

u=ln(x+1)

And,

dv=3dx

Therefore,

du=1x+1

And,

v=(3)dx=3x

Thus, use the formula of integration by parts,

udv=uvvdu

To obtain the integral as,

C(x)=(1+3ln(x+1))dx

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