Maharashtra State BoardHSC Commerce 12th Board Exam
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The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing. - Mathematics and Statistics

Sum

The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing.

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Solution

Let C be the total cost function and R be the revenue

∴ C = 180 + 4x

Now, Revenue = Price × Demand

∴ R = P × x = (240 - x)x

∴ R = 240x - x2

∴ `"dR"/"dx" = 240 - 2"x" = 2(120 - "x")`

Since revenue R is an increasing function, `"dR"/"dx"` > 0

∴ 2(120 - x) > 0

∴ 120 - x > 0

∴ 120 > x

∴ x < 120 

∴ The revenue is increasing for x < 120.

Concept: Application of Derivatives to Economics
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Applications of Derivatives
Exercise 4.4 | Q 4.1 | Page 112
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