Maharashtra State BoardHSC Commerce 12th Board Exam
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A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing. - Mathematics and Statistics

Sum

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing.

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Solution

Let C be the total cost function.

∴ C = 40 + 2x

Revenue = Price × Demand

∴ `"R" = "p" × "x" = (120 - "x") * "x"`

∴ R = 120x - x2

∴ `"dR"/"dx" = 120 - 2"x" = 2(60 - "x")`

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

∴ 2(60 - x) > 0

∴ 60 - x > 0

∴ 60 > x

∴ x < 60 

∴ The revenue R is increasing for x < 60.

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 12.1 | Page 113
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