Application of Integration in business and economics

Ram Lama

Student

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A company sells a product at a price of $20 per unit. The number of units sold per week is modeled by the function �(�)=100−2�, where � is the time in weeks. Find the revenue function and calculate the total revenue generated over the first 8 weeks.

  • 26 Dec, 2023
Replies (1)
Harit Thakuri

Instructor

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Solution: The revenue function (�(�)) is given by the product of the price per unit and the quantity sold: �(�)=�(�)⋅�(�) where �(�) is the price per unit, and �(�) is the quantity sold.

In this case, �(�)=20 and �(�)=100−2�. Therefore, �(�)=20(100−2�)

To find the total revenue over the first 8 weeks, we integrate �(�) from 0 to 8: Total Revenue=∫08�(�) ��

Total Revenue=∫0820(100−2�) ��

Solving this integral will give the total revenue.

:) Happy Learning

  • 26 Dec, 2023

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