flat increase v.s. percentage increase

[RoboEmperor]

I'm trying to use math to optimize a video game strategy but I'm stumped at how to approach this mathematically.
This is the equation
z = 6.6x * 1.066y

So I'm trying to figure out when it's more optimal to increase x and when it's more optimal to increase y. By "more optimal" I mean increase z by the largest amount.

I can just brute force this like a caveman but i rather work smarter than harder so could somebody teach me how to solve problems like this?

Thanks.

 

[RoboEmperor]

slight correction, the equation is z = 6.6x * (1 + 0.66y)

 

[Dr.Peterson]

Are you asking whether increasing x by 1 or increasing y by 1 will yield the larger increase in z? Why not just try it?

Does "when" refer to how large the increase is, or what x and y are, or what? And are the particular numbers only an example, so that you are really asking more generally?

Suppose you are talking about an increase of 1. Then the two options will yield z = 6.6(x+1) * (1 + 0.66y) and z = 6.6x * (1 + 0.66(y+1)), and you are asking to solve the inequality 6.6(x+1) * (1 + 0.66y) > z = 6.6x * (1 + 0.66(y+1)) to find the condition under which increasing x is better.

If that's what you want, what happens when you solve it?

 

[RoboEmperor]

Argh, mistakes everywhere, the real equation is z = 6.6x * (1 + 0.066y) (forgot a 0, y increases yield by 6.6% not 66%)
Just for my brain's sake, I simplified the equation to z = 6x (1+0.06y)

So solving the inequality 6(x+1) (1+0.06y) > 6x(1+0.06(y+1))

x<(0.36y+6)/(0.36)
y>(0.36x-6)/(0.36)

And putting this in a graphing calculator, y+1 > x+1 when x = 17. And then we alternate between increasing y and x for the optimal result since the graph is linear.

Thanks!