Compute the Minimum Value Of $f ( x , y , z ) = x ^ { 2 } + y + z ^ { 2 }$

question 261

Essay

Compute the minimum value of $f ( x , y , z ) = x ^ { 2 } + y + z ^ { 2 }$ subject to the condition that $g ( x ) = 2 x + y + 4 z = 6$ .

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Definitions:

Higher Inflation

Higher Inflation occurs when there is a sustained increase in the general price level of goods and services, reducing purchasing power over time.

Long Run

A period in economics where all inputs can be adjusted, and companies can change all factors of production.

Phillips Curve

An economic model suggesting an inverse relationship between rates of unemployment and corresponding rates of inflation.

Unemployment Rate

The percentage of the labor force that is jobless and actively seeking employment within an economy.