Use Lagrange Multipliers to Find the Given Extremum $x$ And $y$ Are Positive

question 27

Multiple Choice

Use Lagrange multipliers to find the given extremum. Assume that $x$ and $y$ are positive. Minimize $f ( x , y ) = e ^ { xy }$ Constraint $x ^ { 2 } + y ^ { 2 } - 8 = 0$

• A) \(f ( 2,2 ) = e ^ { 4 }\)
• B) \(f ( 1,1 ) = e ^ { 1 }\)
• C) \(f ( 3,1 ) = e ^ { 3 }\)
• D) \(f ( 4,2 ) = e ^ { 8 }\)
• E) \(f ( 2,1 ) = e ^ { 2 }\)

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Definitions:

Special-Interest Effect

The impact of a small, concentrated interest group on policy-making, often at the expense of broader public interest.

Principal-Agent Problem

A dilemma in economics where one party (the agent) is expected to act in the best interest of another (the principal) but may not do so due to conflicting interests.

Adverse Selection Effect

A situation in which asymmetric information leads to the selection of undesired risks, often seen in insurance markets where customers know more about their health status than insurers.