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If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4

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प्रश्न

If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4

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उत्तर

The supply function p = 3x + 5x²

When x = 4

⇒ p = 3(4) + 5(4)²

p = 12 + 5(16)

= 12 + 80

p = 92

∴ x0 = 4 and p0 = 92

Producer’s Surplus

P.S = `x_0"p"_0 - int_0^(x_0) "g"(x)  "d"x`

= `(4)(92) - int_0^4 (3x + 5x^2) "d"x`

= `368 - [(3x^2)/2 + (5x^3)/3]_0^4`

= `368 - {(3/2 (4)^2 + 5/3 (4)^3) - [0]}`

= `368 - {3/2 (16) + 5/3 (64)}`

= `368 - [24 + 320/3]`

= `368 - 24 - 320/3`

= `344 - 320/3`

= `(1032 - 320)/3`

= `712/3`

= `237.3`

∴PS =  237.3 units

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Application of Integration in Economics and Commerce
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Integral Calculus – 2 - Exercise 3.3 [पृष्ठ ७५]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 3 Integral Calculus – 2
Exercise 3.3 | Q 6 | पृष्ठ ७५

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