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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 The marginal cost for a catering service to cater to x people can be modeled by

d C d x = 20 x x 2 + 1000 .

When x = 200, the cost C (in dollars) is $4049.69.

Find the cost function.

Find the costs of catering to 500 people and 1000 people.

(a)

To determine

To calculate: The cost function for a catering service that can be modeled by dCdx=20xx2+1000.

Explanation

Given Information:

The rate of change of the cost function with respect to people;

dCdx=20xx2+1000.

The initial condition C(200)=$4049.69

Here people is x and output (in hours) is C.

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:

Consider the derivative:

dCdx=20xx2+1000

Apply, integration on both sides:

dCdxdx=20xx2+1000dx+C=10(x2+1000)

(b)

To determine

To calculate: The cost of catering to 500 people and 1000 people.

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