I'm not that familiar with English math terminology so I hope that you'll bear with me.

Currently, I'm trying to maximize a function with two constraints, but I got stuck because of one of my constraints. My first constraint has both the variables

*x*and

*y*, but my second constraint only has the variable

*y*. The reason why I'm confused by this is that when I proceed to solve the problem, I have no use for the Lagrange multiplier

*λ*. I can simply solve the partial differential for

*λ*

_{1}and

*λ*

_{2}. This will enough to yield my results (the

*x*and

*y*coordinates). It is frustrating me because I need to put it into words, what I am doing (in terms of using Lagrange multipliers) and why I apparently had to skip the

*λ*all together.

The function that I'm trying to maximize is as follows:

(, ) = −0,01

^{2}+ 395 + 100

My constraints are these:

2 + ≤ 44,000

≤ 20,000

I know that the correct answer (through using other methods) is:

*x = 12,000*

y = 20,000

y = 20,000

The way that I've proceeded to solve this problem is by putting the respective functions and constraints into an algorithm:

L(x ,y,

*λ*

_{1},

*λ*

_{2}) = −0,01

^{2}+ 395 + 100 -

*λ*

_{1}* (2 + - 44,000) -

*λ*

_{2}* ( - 20,000)

Then finding the partial differentials of

*x*,

*y*,

*λ*

_{1}and

*λ*

_{2}to ultimately isolate

*x*and

*y*. I am getting the correct results, but there's no need to find the partial differentials of

*x*and

*y*?