Maximizing two variables

Question

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?

Answer 1

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 $y_i$