Finding the Optimal Ratio between X and Y for Maximum Revenue

[the_dialogue]

I have an array of data such as:

X---------Y-----------Z
0---------3--------1000
10-------3---------2000
etc.

X and Y are constituents in a material that I must create. Z is the revenue that we earn from having X and Y as constituents. However, there is always some exchange rate between X and Y; so there must be a ratio like:
X=kY, where k is a constant. This would signify that adding 'k' multiple of Y is equivalent (will produce the same revenue) as adding 1 of X.

This problem, as simple as it may seem, does not seem to sink into my head. Do you have any suggestions on how to determine this 'ratio' between X and Y?

I thought of determining which 2 pairs of X and Y give the same revenue, and then comparing those. For example:
(x,y) --> (10,3) produces revenue of 1000
and ---> (15,0) produces revenue of 1000.
Therefore, 5 of X is equivlant to 3 of Y. So, 5X=3Y and X = 3/5Y.

Any help is appreciated.

 

[Office_Shredder]

Your method looks good to me. You could also just find the net worth of adding x or y... for example, from the data you supplied, it appears as if one x is equivalent to getting 100 Z (although the data may not be linear, I don't have the original question in front of me, so that would be your judgement call). Solving for Y also gives you your ratio

 

[Architeuthis Dux]

I understand the importance of finding the optimal ratio between X and Y for maximum revenue. It is a crucial aspect in material creation and can greatly impact the success of a project. I would suggest using a mathematical approach to determine the ratio between X and Y.

One method could be through regression analysis. This involves analyzing the relationship between the independent variable (X) and the dependent variable (Z) to find the best-fitting line that represents the data. In this case, the slope of the line would represent the ratio between X and Y.

Another approach could be through trial and error. You could start with a certain ratio and observe the resulting revenue. If it is not optimal, adjust the ratio and repeat the process until you find the ratio that produces the maximum revenue. This method may be more time-consuming, but it can also provide valuable insights and understanding of the relationship between X and Y.

Additionally, you could also consider consulting with experts or conducting further research in the field to gain a better understanding of the relationship between X and Y and how it affects revenue. This could also help in determining the optimal ratio.

Overall, finding the optimal ratio between X and Y for maximum revenue requires a combination of mathematical analysis, experimentation, and research. I hope my suggestions will help guide you in your research and lead to successful results.