Explanation Given Information: The latest solid state drive is expected to sell between q = 180 , 000 − p 2 and q = 200 , 000 − p 2 units if priced at p dollars and the price is planned to be set between $ 300 and $ 400 . Formula used: The value of the integral ∬ R f ( x , y ) d x d y is ∫ a b ( ∫ c ( x ) d ( x ) f ( x , y ) d y ) d x where the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . The average value of a function f ( x , y ) on the region R is f ¯ = 1 A ∬ R f ( x , y ) d x d y where A is the area of the region, A = ∬ R d x d y . Calculation: Consider the latest solid state drive is expected to sell between q = 180 , 000 − p 2 and q = 200 , 000 − p 2 units if priced at p dollars and the price is planned to be set between $ 300 and $ 400 . Since, revenue is product of price and quantity. Let p q = f ( x , y ) and the region is 300 ≤ p ≤ 400 and 180 , 000 − p 2 ≤ q ≤ 200 , 000 − p 2 , since y is represented in thousands of dollars. Thus, calculate ∬ R f ( x , y ) d x d y . Recall that the value of the integral ∬ R f ( x , y ) d x d y is ∫ a b ( ∫ c ( x ) d ( x ) f ( x , y ) d y ) d x where the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . Thus, ∬ R f ( x , y ) d x d y = ∫ 300 400 ( ∫ 180 , 000 − p 2 200 , 000 − p 2 p q d q ) d p . Simplify the integral ∫ 300 400 ( ∫ 180 , 000 − p 2 200 , 000 − p 2 p q d q ) d p with respect to q . ∫ 300 400 ( ∫ 180 , 000 − p 2 200 , 000 − p 2 p q d q ) d p = ∫ 300 400 [ p q 2 2 ] q = 180 , 000 − p 2 200 , 000 − p 2 d p = ∫ 300 400 [ p ( 200 , 000 − p 2 ) 2 − ( 180 , 000 − p 2 ) 2 2 ] d p = 1 2 ∫ 300 400 [ p ( 200 , 000 − p 2 ) 2 − p ( 180 , 000 − p 2 ) 2 ] d p Simplify the integral with respect to p . 1 2 ∫ 300 400 [ p ( 200 , 000 − p 2 ) 2 − p ( 180 , 000 − p 2 ) 2 ] d p = 1 12 [ − ( 200 , 000 − p 2 ) 3 + ( 180 , 000 − p 2 ) 3 ] p = 300 400 = 1 12 [ − ( 200 , 000 − 400 2 ) 3 + ( 180 , 000 − 300 2 ) 3 ] = 1 12 [ − ( 200 , 000 − 160 , 000 2 ) 3 + ( 180 , 000 − 90 , 000 2 ) 3 ] = 4

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 8.5, Problem 44E

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To calculate: The average value of all possible revenues you can make if the latest solid state drive is expected to sell between q=180,000−p2 and q=200,000−p2 units if priced at p dollars and the price is planned to be set between $300 and $400.

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The average value of all possible revenues you can make if the latest solid state drive is expected to sell between q = 180 , 000 − p 2 and q = 200 , 000 − p 2 units if priced at p dollars and the price is planned to be set between $ 300 and $ 400 .

Solution Summary: The author calculates the average value of all possible revenues if the latest solid state drive is expected to sell between q=180,000-p2 and

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To calculate: The average value of all possible revenues you can make if the latest solid state drive is expected to sell between q=180,000−p2 and q=200,000−p2 units if priced at p dollars and the price is planned to be set between $300 and $400.

Chapter 8 Solutions