
#1
Feb2106, 07:23 PM

P: 23

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?




#2
Feb2106, 07:42 PM

HW Helper
P: 1,007

Would you be more confortable using the method of Lagrange Multipliers or using the substitution/partial derivatives=0 and the D=FxxFyyFxy^2 second derivative test thinggy?




#3
Feb2106, 07:50 PM

P: 23

definitely using second derivative test thingy




#4
Feb2106, 08:08 PM

P: 23

Multivariable Optimization Problem
Got the idea. You set z=120xy 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=120xy... and you get x, y and z equal 40.



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