   Chapter 5.3, Problem 12QY ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# The marginal cost of producing x units of a product is modeled by d C d x = 16 − 0.06 x . It costs $25 to produce one unit. Find (a) the cost function C (in dollars), (b) the fixed cost (when x = 0), and (c) the total cost of producing 500 units. (a) To determine To calculate: The marginal cost of producing x units of a product. Explanation Given Information: The marginal cost of producing x units of a product of is modeled by dCdx=160.06x The cost of one units is$25.

C(1)=\$25

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

The marginal cost of producing x units of a product:

dCdx=160.06x

Apply, integration on both sides:

dC(x)dxdx=(160

(b)

To determine

To calculate: The marginal fixed cost of producing no units of a product.

(c)

To determine

To calculate: The total cost of producing 500 units.

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