# A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which revenue is increasing Solution: Total cost C = 40 + - Mathematics and Statistics

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

Solution: Total cost C = 40 + 2x and Price p = 120 – x

Revenue R = square

Differentiating w.r.t. x,

∴ ("dR")/("d"x) = square

Since Revenue is increasing,

∴ ("dR")/("d"x) > 0

∴ Revenue is increasing for square

#### Solution

Total cost C = 40 + 2x and Price p = 120 – x

Revenue R = px

= (120 – x)x

∴ R = 120 – x2

Differentiating w.r.t. x,

("dR")/("d"x) = 120 – x

Since Revenue is increasing,

("dR")/("d"x) > 0

∴ 120 – 2x > 0

∴ 120 > 2x

∴ x < 60

∴ Revenue is increasing for x < 60

Concept: Application of Derivatives to Economics
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Chapter 1.4: Applications of Derivatives - Q.6

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