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: R ( x , y ) = 15 + 169 x + 182 y − 5 x 2 − 7 y 2 − 7 x y First, find the critical points of each function. R x = ∂ ∂ x ( 15 + 169 x + 182 y − 5 x 2 − 7 y 2 − 7 x y ) = 169 − 10 x − 7 y R y = ∂ ∂ y ( 15 + 169 x + 182 y − 5 x 2 − 7 y 2 − 7 x y ) = 182 − 14 y − 7 x Substitute R x = 0 and R y = 0 , 169 − 10 x − 7 y = 0 182 − 14 y − 7 x = 0 Solving the above equation, the values of x and y are obtained

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Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 9.3, Problem 41E

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The number of each that should be sold to produce maximum revenue and also maximum revenue for the given function R(x,y)=15+169x+182y−5x2−7y2−7xy.

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Chapter 9.3, Problem 40E

Chapter 9.4, Problem 1YT

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Chapter 9 Solutions

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The number of each that should be sold to produce maximum revenue and also maximum revenue for the given function R ( x , y ) = 15 + 169 x + 182 y − 5 x 2 − 7 y 2 − 7 x y .

Solution Summary: The author explains that the number of each that should be sold to produce maximum revenue is 12 and 7, and the maximal revenue for the given function is 166600.

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To find:

The number of each that should be sold to produce maximum revenue and also maximum revenue for the given function R(x,y)=15+169x+182y−5x2−7y2−7xy.

Want to see the full answer?

Chapter 9 Solutions

The number of each that should be sold to produce maximum revenue and also maximum revenue for the given function R ( x , y ) = 15 + 169 x + 182 y − 5 x 2 − 7 y 2 − 7 x y .

Solution Summary: The author explains that the number of each that should be sold to produce maximum revenue is 12 and 7, and the maximal revenue for the given function is 166600.

Concept explainers

Videos

To find: The number of each that should be sold to produce maximum revenue and also maximum revenue for the given function R(x,y)=15+169x+182y−5x2−7y2−7xy.

Want to see the full answer?

Chapter 9 Solutions

To find:

The number of each that should be sold to produce maximum revenue and also maximum revenue for the given function R(x,y)=15+169x+182y−5x2−7y2−7xy.