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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Cost A company produces a product for which the marginal cost of producing x units is modeled by d C / d x = 2 x 12 and the fixed costs are $125.

(a) Find the total cost function and the average cost function.

(b) Find the total cost of producing 50 units.

(c) In part (b), how much of the total cost is fixed? How much is variable? Give examples of fixed costs associated with the manufacturing of a product. Give examples of variable costs.

(a)

To determine

To calculate: The total cost function and the average cost function for the model dCdx=2x12 product where C is the marginal cost and x represents number of product manufacture by a company and the fixed costs are $125.

Explanation

Given Information:

The provided model for the marginal cost to produce x units is dCdx=2x12 and the fixed costs are $125.

Formula used:

The simple power rule of integration xndx=xn+1n+1+C, where n1.

The average cost is given as, C¯(x)=C(x)x.

Calculation:

Consider the model of the marginal cost and number of units, dCdx=2x12.

Integrate the provided model, use the sum or difference rule of integration, (f(x)±g(x))dx=f(x)dx±g(x)dx.

dCdxdx=(2x12)dxC(x)=2xdx12dx

Integrate further use the simple power rule of integration, xndx=xn+1n+1+C.

C(x)=2[x1+11+1]12x+C=x212x+C

The fixed cost means the cost to produce zero units

(b)

To determine

To calculate: The total cost to produce 50 units.

(c)

To determine

To calculate: The fixed cost in the total cost and the variable cost in the total cost and also gives example of fixed costs and variable costs that are associated with the company.

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