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