Multivariable Optimization Problem

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Homework Help Overview

The problem involves optimizing the sum of products of three numbers that add up to 120. The original poster seeks assistance in formulating and beginning the problem related to multivariable optimization.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss different methods for solving the optimization problem, including the method of Lagrange Multipliers and the second derivative test. There is also a suggestion to express one variable in terms of the others to simplify the problem.

Discussion Status

The discussion is progressing with participants sharing their preferred methods and approaches. One participant has outlined a potential path to derive the necessary equations, indicating a productive direction in the exploration of the problem.

Contextual Notes

There is an emphasis on maximizing the sum of products under the constraint that the three numbers must sum to 120. The specific methods mentioned reflect varying levels of comfort with mathematical techniques.

Black Orpheus
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I need to "write the number 120 as a sum of three numbers so that the sum of the products taken two at a time is a maximum." I think this means that x+y+z=120 and xy+xz+yz=maximum. Can someone help me begin this problem?
 
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Would you be more confortable using the method of Lagrange Multipliers or using the substitution/partial derivatives=0 and the D=FxxFyy-Fxy^2 second derivative test thinggy?
 
definitely using second derivative test thingy
 
Got the idea. You set z=120-x-y and plug it into xy+xz+yz, which is then f(x,y). So you take the derivative of that, set the partials equal to 0, solve for x, solve for y, plug those back into z=120-x-y... and you get x, y and z equal 40.
 

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