   Chapter 5, Problem 101RE ### 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 modelR = 70 for 10 years. Over the same period of time, the cost (in millions of dollars) is projected to follow the model C   =   30   +   0.3 t 2 where t is the time (in years). Approximate the profit over the 10-year period.

To determine

To calculate: The profit in the 10 years if the revenue from the manufacturing process is followed by the model R=70 and the cost model is given by C=30+0.3t2.

Explanation

Given information:

The revenue from the manufacturing process is followed by the model R=70 for 10 years and the cost model is given by C=30+0.3t2. Where t is time

Formula used:

Profit can be calculated as,

Profit=RevenueCost

Change in profit can be calculated as,

x1x2dRdxdx=R(x2)R(x1)

Calculation:

Consider the revenue model R=70 and cost model C=30+0.3t2

To determine the profit, subtract revenue from the cost as shown below,

Profit=RevenueCost=70(30+0.3t2)=400

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