# Maximizing two variables

If I wanted to maximize two variables can I just rank the two variables from the sample as a point system and then sum the points? I know this probably isn't the most mathematically correct way. For example, if I have an average and a variance for 150 different samples from one population and I rank each average and variance and then add the points from both rankings could I maximize the sum?

• What does maximising variables mean? Jun 6, 2019 at 17:52
• @copper.hat I want to maximize average and variance Jun 6, 2019 at 18:32
• @copper.hat and instead of trying to write a multivariate optimization program I was wondering if you could just rank each variable using a point system and then just sum the points and maximize Jun 6, 2019 at 18:33
• Can you write an expression for what your ranking and point system would be? Also can you clarify - do you have 1 average across 150 samples or are you saying you have 150 averages? Jun 6, 2019 at 21:50
• Also, I agree with copper.hat. I'm not sure what your variables are. Jun 6, 2019 at 22:08

Based on our conversation in the comments of your post (=trying to find the data point with the highest combo of 2 components), yes, it would be correct to calculate the combination for each data point, order these, and select the highest value.

For example, if $$\alpha \in [0,1]$$ were the weight of the $$x$$ components, you could

• Calculate the score for each data point as $$z_i, \forall i\in 1..150$$:

$$\alpha*x_1+(1-\alpha)*y_1 = z_1$$

$$\alpha*x_2+(1-\alpha)*y_2 = z_2$$

and so on until $$z_{150}$$

• Order all the values of $$z_i$$ from highest to lowest.
• Select the highest value of $$z_i$$ and find the associated $$x_i$$ and $$y_i$$