Explanation Approach: For a function z = f ( x , y ) , let f x x , f y y , and f x y all exist in a circular region contained in the xy -plane with center ( a , b ) . Further, let f x ( a , b ) = 0 and f y ( a , b ) = 0 . Define the number D , known as the discriminant, by D = f x x ( a , b ) ⋅ f y y ( a , b ) − [ f x y ( a , b ) ] 2 Then, a. f ( a , b ) is a relative maximum if D > 0 and f x x ( a , b ) < 0 . b. f ( a , b ) is a relative minimum if D > 0 and f x x ( a , b ) > 0 . c. f ( a , b ) is a saddle point (neither a maximum nor a minimum) if D < 0 . d. if D = 0 , the test gives no information. Calculation: Consider the given equation, P ( x , y ) = 1500 + 36 x − 1.5 x 2 + 120 y − 2 y 2 First, find the critical points of each function, P x = ∂ ∂ x ( 1500 + 36 x − 1.5 x 2 + 120 y − 2 y 2 ) = 36 − 3 x P y = ∂ ∂ y ( 1500 + 36 x − 1.5 x 2 + 120 y − 2 y 2 ) = 120 − 4 y Substitute P x = 0 and P y = 0 ,

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.3, Problem 38E

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The value of x and y that maximize the profit and also maximum profit for the given function P(x,y)=1500+36x−1.5x2+120y−2y2.

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Chapter 9.3, Problem 37E

Chapter 9.3, Problem 39E

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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The value of x and y that maximize the profit and also maximum profit for the given function P ( x , y ) = 1500 + 36 x − 1.5 x 2 + 120 y − 2 y 2 .

Solution Summary: The author calculates the value of x and y that maximize the profit and also maximum profit for the given function P(x,y)=1500+36x-1.5x2+

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To find:

The value of x and y that maximize the profit and also maximum profit for the given function P(x,y)=1500+36x−1.5x2+120y−2y2.

Want to see the full answer?

Chapter 9 Solutions

The value of x and y that maximize the profit and also maximum profit for the given function P ( x , y ) = 1500 + 36 x − 1.5 x 2 + 120 y − 2 y 2 .

Solution Summary: The author calculates the value of x and y that maximize the profit and also maximum profit for the given function P(x,y)=1500+36x-1.5x2+

Videos

To find: The value of x and y that maximize the profit and also maximum profit for the given function P(x,y)=1500+36x−1.5x2+120y−2y2.

Want to see the full answer?

Chapter 9 Solutions

To find:

The value of x and y that maximize the profit and also maximum profit for the given function P(x,y)=1500+36x−1.5x2+120y−2y2.