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Which of the Following Pairs of Values (X, Y) Maximizes $f ( x , y ) = x + 3 y$

question 84

Multiple Choice

Which of the following pairs of values (x, y) maximizes the function $f ( x , y ) = x + 3 y$ subject to the constraint $x ^ { 2 } + 9 y ^ { 2 } = 72$ assuming x and y are positive?
(I) (-6, -2) $Which of the following pairs of values (x, y) maximizes the function f ( x , y ) = x + 3 y subject to the constraint x ^ { 2 } + 9 y ^ { 2 } = 72 assuming x and y are positive? (I) (-6, -2) (II) \left( 8 , \sqrt { \frac { 8 } { 9 } } \right) III) (2, -6) (IV) (6, 2) A) III only B) I and II C) IV only D) I only E) none of these$
(II) $\left( 8 , \sqrt { \frac { 8 } { 9 } } \right)$ $Which of the following pairs of values (x, y) maximizes the function f ( x , y ) = x + 3 y subject to the constraint x ^ { 2 } + 9 y ^ { 2 } = 72 assuming x and y are positive? (I) (-6, -2) (II) \left( 8 , \sqrt { \frac { 8 } { 9 } } \right) III) (2, -6) (IV) (6, 2) A) III only B) I and II C) IV only D) I only E) none of these$
III) (2, -6) $Which of the following pairs of values (x, y) maximizes the function f ( x , y ) = x + 3 y subject to the constraint x ^ { 2 } + 9 y ^ { 2 } = 72 assuming x and y are positive? (I) (-6, -2) (II) \left( 8 , \sqrt { \frac { 8 } { 9 } } \right) III) (2, -6) (IV) (6, 2) A) III only B) I and II C) IV only D) I only E) none of these$
(IV) (6, 2)

Understand and apply appropriate methods to calculate the mean of a dataset.

Understand and apply appropriate methods to calculate the median of a dataset.

Apply rounding rules correctly according to standard mathematical conventions.

Calculate the quotient of numbers to the required decimal places and round the result accurately.

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Accurate Generalizations

Statements or conclusions based on evidence and reasoning that correctly represent the characteristics of a broader group.

Nationally Acclaimed

Acknowledged or praised by a broad audience or authoritative bodies across a country.

Standard Deviation

A statistical measure that quantifies the amount of variation or dispersion of a set of data values from the mean.

Ordinary Events

Ordinary events are commonplace occurrences or routines that form part of everyday life, lacking extraordinary or exceptional features.

Which of the Following Pairs of Values (X, Y) Maximizes f(x,y)=x+3yf ( x , y ) = x + 3 yf(x,y)=x+3y

Definitions:

Which of the Following Pairs of Values (X, Y) Maximizes $f ( x , y ) = x + 3 y$