Find the maximum value to this function
Budget $30-250 USD
The constant product for a stablepool at Solidex Automated Market maker is:
(xy)*(x^2 + y^2) = k
where x is the reserves of token0 and y is the reserves of token1. This constraint must always be upheld when the user performs an exchange. We are interested in finding the change in x that produces the maximum value dy. In more simpler terms; We want to find the amount to sell, so that we will get the maximum amount out. x is reserves and token in, and y is reserves and token out.
We rewrite to include the change in reserves, we sell amount dx and obtain amount dy.
The constraint must hold:
(x + dx)*(y-dy)*((x + dx)^2 + (y - dy)^2) = k
I believe this can also be written as such:
y * (x+dx)^3 + x*(y - dy)^3 = k
It is negative dy and positive dx because the constraint must be upheld for the pool's inventory. So after an exchange, dy has left the pool, and dx has increased the pool.
Here is the task I expect delivery on:
Find the function that provides the maximum dy with respect to dx, x and y as parameters. I require a formula answer, not an algorithmic approach.
In more simpler terms; Which dx maximizes dy? Use dx, x and y as inputs that gives dy as output
18 freelancers are bidding on average $86 for this job
Hi, I am Maths tutor with years of experience in my field. I have understand your requirements and think myself suitable for the job. I have done many projects regarding problems solution in Advance Mathematics and Eng More
Hi, I am a professional electrical engineer with having a very strong command of MATLAB and Simulink. I have an experience of over 8 years. I can help you out with this perfectly. Check my portfolio for my samples. Hir More
hi I have read your description carefully. I have rich experiences in ⭐ MATLAB, R, Mathematica, math, Optimization. ⭐ I worked on many similar projects. I can guarantee the quality of the job. Please kindly message me. More
Hey there! I'm a professional expert in mathematics having more than 5 years of experience. I've read your description and I can do your task perfectly.
----------------- Hey, I'm interested in your project. Please send me a message so that we can discuss more. ----------------------------
Hi. How are you? I have just read your proposal and I am sure I can complete the project on time. I am a mathematician who has 15 years of experiences in Numerical Analysis using Matlab/Python/R, .... Please contact m More
Dear I'm interested to discuss more about your project after reading your description. I am Program developer with 7 years of experience. I have many experiences working on similar projects to develop optimization prog More
Dear Client! How are you? Thanks for your job posting I read your job description carefully I am an Math expert I have a lots of experience in this field If you work with me, you will get best good results Please give More