Use Lagrange Multipliers to Find the Minimum Value of the Function

question 76

Short Answer

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints. $f ( x , y , z , t ) = 5 x + 5 y + 5 z + 5 t , \quad 5 \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + t ^ { 2 } \right) = 4$

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Definitions:

Annuity

A monetary scheme providing regular payment intervals to a person, often employed as a retirement income solution.

Payment Interval

The regular time period between payments on a loan or investment, such as monthly or annually.

Periodic Interest Rate

The interest rate charged or paid over a specific period of time, shorter than a year, such as monthly or quarterly.

Annuity

A financial arrangement designed to supply a consistent stream of payments, usually to assist individuals in maintaining income after retirement.