# 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 elasticity of demand for price ₹ 80. - 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 elasticity of demand for price ₹ 80.

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

p = 120 – x

∴ x = 120 – p

Differentiating w.r.t. p,

("d"x)/("dp") = square

∴ Elasticity of demand is given by η = - "P"/x*("d"x)/("dp")

∴ η = square

When p = 80, then elasticity of demand η = square

#### Solution

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

p = 120 – x

∴ x = 120 – p

Differentiating w.r.t. p,

("d"x)/("dp") = – 1

∴ Elasticity of demand is given by η = - "P"/x*("d"x)/("dp")

∴ η = (-"P")/(120 - "P") (-1)

= "p"/(120 - "P")

When p = 80, then elasticity of demand η = 80/(120 - 80)

= 80/40

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

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