Explanation Given Information: The demand and the supply functions are modelled as p = 60 x 2 + 81 and p = x 3 respectively. Formula used: The formula for the integral ∫ 1 u 2 ± a 2 d u is: ∫ 1 u 2 ± a 2 d u = ln | u ± u 2 ± a 2 | + C The General power of integration rule: ∫ u n d u = u n + 1 n + 1 + C Here, n is the any number. General power differentiation Rule: d d x [ u n ] = n u n − 1 d u d x Calculation: Consider the provided demand and supply functions: p = 60 x 2 + 81 And, p = x 3 Now, Find the equilibrium point by equating functions of demand and supply. 60 x 2 + 81 = x 3 ( 60 ) ( 3 ) = x x 2 + 81 180 = x x 2 + 81 Square both sides. ( x x 2 + 81 ) 2 = ( 180 ) 2 x 2 ( x 2 + 81 ) = 32400 x 4 + 81 x 2 − 32400 = 0 x 4 + 225 x 2 − 144 x 2 − 32400 = 0 Further solve. x 2 ( x 2 + 225 ) − 144 ( x 2 + 225 ) = 0 ( x 2 + 225 ) ( x 2 − 144 ) = 0 Further solve. x 2 − 144 = 0 x 2 = 144 x 2 = 12 2 x = 12 And, x 2 + 225 = 0 x 2 = − 225 x = − 225 = 15 i ( imaginary number ) Substitute 12 for x in expression p = x 3 to calculate the price of product

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 6.2, Problem 61E

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To calculate: The consumer and producer surpluses for the product, when the demand and the supply functions are modelled as p=60x2+81 and p=x3 respectively.

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Chapter 6.2, Problem 60E

Chapter 6.2, Problem 1QY

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Chapter 6 Solutions

Calculus: An Applied Approach (Providence College: MTH 109)

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The consumer and producer surpluses for the product, when the demand and the supply functions are modelled as p = 60 x 2 + 81 and p = x 3 respectively.

Solution Summary: The author calculates the consumer and producer surpluses for the product, when the demand and supply functions are modelled as p=60sqrtx2+81

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To calculate: The consumer and producer surpluses for the product, when the demand and the supply functions are modelled as p=60x2+81 and p=x3 respectively.

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Chapter 6 Solutions