- #1

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- 1,169

- 2

f(x,y,z) = ax + by + cz

with the constrain x+y=k

My book minimizes this function by a way I am not completely familiar with:

dF = adx + bdy + cdz 0

and since dy=-dx we can write:

dF = (a-b)dx + cdz = 0

=>

a-b = c dz/dx (1)

How I would minimize is simply plug y=k-x into the definition of f:

f(x,z) = (a-b)x + bk + cz

And take partial derivatives

df/dx = a-b + cdz/dx

df/dz = (a-b) dx/dz + c

And seting both equal to zero yields a system of equations which does not reduce to (1).

What is wrong?