   Chapter 5.5, Problem 55E ### 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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# Cost, Revenue, and Profit The revenue (in millions of dollars) from a manufacturing process is projected to follow the model R =   100 for 10 years. Over the same period of time, the cost (in millions of dollars) is projected to follow the model C   = 60   +   0.2 t 2 , where t is the time (in years). Approximate the profit over the 10-year period.

To determine

The profit (in millions of dollars) from a manufacturing process over the 10-year period, if the revenue is projected to follows the model R=100 and the cost is projected to follows the model C=60+0.2t2.

Explanation

Given Information:

The revenue (in millions of dollars) from a manufacturing process over the 10-year period is projected to follows the model R=100. The cost (in millions of dollars) is projected to C=60+0.2t2, here, t is the time in years.

Formula used:

Area of a region bounded between the two graphs is,

If f and g are continuous function over the region [a,b] and g(x)f(x) for all value of x in [a,b]. The area of the region bounded by the graphs of the function f, g, from x=a to x=b is given by,

A=ab[f(x)g(x)]dx

Calculation:

Consider the revenue function,

R=100

And, the cost function

C=60+0.2t2

The profit over the 10-year period will be equal to the area bounded by the graphs of revenue function and cost function. The area between two graphs is the profit over the 10-year,

Profit=010[RC]dt=010[100(60+0

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