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Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

Calculate consumer’s surplus if the demand function p = 122 – 5x – 2x2, and x = 6

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Question

Calculate consumer’s surplus if the demand function p = 122 – 5x – 2x2, and x = 6

Sum
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Solution

Demand function p = 122 – 5x – 2x2 and x = 6

When x = 6

p = 122 – 5(6) – 2(6)2

= 122 – 30 – 2(36)

= 122 – 102

= 20

∴ p0 = 20

.S = `int_^x` (demand function) dx – (Price × quantity demanded) 

- `int_0^6` (122 – 5x – 2x2) dx – (20 × 6)

= `[122x - 5(x^2/2) - 2(x^3/3)]_0^6 - 120`

= `[122(6) - ((6)^2/2) - 2((6)^3/3) - [0]] - 120`

= `[732 - ((5(36))/2) - ((2(216))/3)] - 120`

= [732 – 5(18) – 2(72)] – 120

= 732 – 90 – 144 – 120

= 732 – 354

= 378

∴ CS = 378 units

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Application of Integration in Economics and Commerce
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Chapter 3: Integral Calculus – 2 - Exercise 3.3 [Page 75]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 3 Integral Calculus – 2
Exercise 3.3 | Q 2 | Page 75

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