How to find combination of two values such that the ratio and sum of those is fixed to certain numbers with R

Question

How can I find all combination of two numbers such that the sum of the two values amount to tot_max <= 16 (max, less is allowable) and ratio between the two is rat=0.5.

Instance of such is:

V1 V2 ratio(V1/V2) sum
1  2   0.5          3.   OK
2  4   0.5          6.   OK
3  6   0.5          9.   OK
4  8   0.5         12.   OK
8  16  0.5         24.   NOT OK (over 16)

These two numbers (V1 and V2) should be integer and greater than 0.

How can I create a R code so that it can accommodate different values of tot_max and rat?

Answer 1

This is a math problem and not necessarily programing

You have x + y < 16 and x/y = 0.5 and x, y > 0. with these three two conditions, doing algebra gives you: 1 <= x <= 5 and y = 2x.

therefore:

x <- seq(5)
y <- 2*x
data.frame(x, y, sum = x+y, ratio = x/y) 

  x  y sum ratio
1 1  2   3   0.5
2 2  4   6   0.5
3 3  6   9   0.5
4 4  8  12   0.5
5 5 10  15   0.5
 

Answer 2

df <- expand.grid(V1=1:15, V2=1:15)
df <- df[ df$V1 + df$V2 <= 16 & df$V1 / df$V2 == 0.5, ]
df
#>     V1 V2
#> 16   1  2
#> 47   2  4
#> 78   3  6
#> 109  4  8
#> 140  5 10