Use Lagrange Multipliers to Minimize the Function $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$

question 83

Multiple Choice

Use Lagrange multipliers to minimize the function $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ subject to the following constraint. $x + y + z - 21 = 0$ Assume that x, y, and z are positive.

• A)49
• B)147
• C)98
• D)294
• E)441

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Definitions:

Economic Stabilization

Efforts or policies aimed at maintaining economic growth, controlling inflation, and reducing unemployment to achieve a stable economy.

Discretionary Policies

Economic strategies and decisions made by a government that can be altered or adjusted in response to changing economic conditions.

Milton Friedman

A prominent American economist known for his strong belief in free-market capitalism and for being a leading proponent of monetarism in economic policy.

Monetarist

An economic theory that emphasizes the role of governments in controlling the amount of money in circulation as the primary method for ensuring economic stability and growth.