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Find the price, if the marginal revenue is 28 and elasticity of demand is 3.

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प्रश्न

Find the price, if the marginal revenue is 28 and elasticity of demand is 3.

योग
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उत्तर

Given, marginal revenue (Rm) = 28 and
elasticity of demand (η) = 3

`"R"_"m" = "P"(1 - 1/eta)`

∴ `28 = "P" (1 - 1/3)`

∴ 28 = `"P" (2/3)`

∴ `(28 xx 3)/2` = P

∴ P = 42

∴ price = ₹ 42

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अध्याय 4: Applications of Derivatives - Exercise 4.4 [पृष्ठ ११२]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 4 Applications of Derivatives
Exercise 4.4 | Q 7.2 | पृष्ठ ११२

संबंधित प्रश्न

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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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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 also find an elasticity of demand for price 80.


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If the marginal revenue is 50 and the price is ₹ 75, then elasticity of demand is 4


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


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`


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

Profit π = R – C

∴ π = `square`

Differentiating w.r.t. x,

`("d"pi)/("d"x)` = `square`

Since Profit is increasing,

`("d"pi)/("d"x)` > 0

∴ Profit is increasing for `square`


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∴ x = 120 – p

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

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