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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5, Problem 102RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

Cost, Revenue, and Profit Repeat Exercise 101 for revenue and cost models given by

R =   70   +   0.1 t

and

C   =   30   +   0.3 t 2.

Did the profit increase or decrease? Explain why.

To determine

To calculate: Whether the profit increase or decrease over the 10 years where the previous revenue was $300 million. If the revenue is R=70+0.1t and the cost model is C=30+0.3t2.

Explanation

Given information:

The revenue is R=70+0.1t for 10 years and the cost model is given by C=30+0.3t2. The previous revenue was $300 million when R=70 and the cost model is given by C=30+0.3t2. Here t stands for time.

Formula used:

Profit can be calculate as

Profit=Revenue−Cost

Change in profit can be calculated as,

∫x1x2dRdxdx=R(x2)−R(x1)

Calculation:

Consider the revenue model R=70+0.1t and cost model C=30+0.3t2

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

Profit=Revenue−Cost=70+0.1t−(30+0.3t2)=40+0.1t−0.3t2

To find approximate profit over the ten year,

∫010(40+0

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