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 profit 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 profit is increasing

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Solution

Now, Profit = Revenue − Total cost

∴ π = R − C

= 240x − x2 − (180 + 4x)

= 240x − x2 − 180 − 4x

∴ π = − x2 + 236x − 180 

∴ `("d"pi)/("d"x)` = −2x + 236 = 2(− x + 118)

Since profit is an increasing function, `("d"pi)/("d"x)` > 0

∴ 2(−x + 118) > 0

∴ − x + 118 > 0

∴ 118 > x

∴ x < 118

∴ The profit is increasing for x < 118.

Concept: Application of Derivatives to Economics
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Chapter 1.4: Applications of Derivatives - Q.5

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