Hi everyone.

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 variablesxandy, but my second constraint only has the variabley. The reason why I'm confused by this is that when I proceed to solve the problem, I have no use for the Lagrange multiplierλ. I can simply solve the partial differential forλ_{1}andλ_{2}. This will enough to yield my results (thexandycoordinates). 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 theλall together.

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

𝑓(𝑥, 𝑦 = −0,01𝑥^{2}+ 395𝑥 + 100

My constraints are these:

2𝑥 + 𝑦 ≤ 44,000

𝑦 ≤ 20,000

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

x = 12,000

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}) = −0,01𝑥^{2}+ 395𝑥 + 100 -λ_{1}* (2𝑥 + 𝑦 - 44,000) -λ_{2}* (𝑦 - 20,000)

Then finding the partial differentials ofx,y,λ_{1}andλ_{2}to ultimately isolatexandy. I am getting the correct results, but there's no need to find the partial differentials ofxandy?