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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)

Definitions:

Proportion

Another way of saying fraction.

Extremes

The highest or lowest level of a math function on an interval.

Proportion

A part or share of a whole, often expressed as a ratio or fraction, indicating the relationship in size or amount between parts.

Means

The average that is derived by adding up all the values of a given series and dividing by the number of values.

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 $f ( x , y ) = x + 3 y$