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

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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"/("d"x)` = 240 – 2x

= 2(120 – x)

Since revenue R is an increasing function, `"dR"/("d"x)` > 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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Chapter 1.4: Applications of Derivatives - Q.5

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