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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, Revenue, and Profit Repeat Exercise 55 for revenue and cost models given by R =   100   +   0.08 t  and  C =   60   +   0.2 t 2 . Did the profit increase or decrease? Explain why.

To determine

The profit (in millions of dollars) from a manufacturing process over the 10-year period, if the revenue is R=100+0.08t and the cost is C=60+0.2t2.

Explanation

Given Information:

The revenue (in millions of dollars) from a manufacturing process over the 10-year period is R=100+0.08t. The cost (in millions of dollars) is 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+0.08t

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. Use the formula for the area between two graphs to calculate the profit over the 10-year period,

Profit=010[RC]dt=010[(100+0.08t)(60+0.2t2)]dt=010[100+0

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