R help - Feb 2012 - Challenge

Hi,

I have the following equation:

x1 + x2 + x3 - 2(x4 + x5 + x6) + 3(x7) = N

each x_i can take any value: 1, 2, 3, 5, 6, 10, 15 or 30 and
each one is different from each other.

Which combination of values ??in the formula which leads to 
the smallest value of N?

How can I program this situation?

--------------------------------------
Silvano Cesar da Costa
Departamento de Estat?stica
Universidade Estadual de Londrina
Fone: 3371-4346

On 22-02-2012, at 13:49, Silvano wrote:
> Hi,
> 
> I have the following equation:
> 
> x1 + x2 + x3 - 2(x4 + x5 + x6) + 3(x7) = N
> 
> each x_i can take any value: 1, 2, 3, 5, 6, 10, 15 or 30 and
> each one is different from each other.
> 
> Which combination of values ??in the formula which leads to the smallest
value of N?
> 
> How can I program this situation?
I hope this isn't homework.

library(gtools)
val <- c(1,2,3,5,6,10,15,30)
x.vals <- permutations(n=length(val),r=7,v=val)
f <- function(x) x[1]+x[2]+x[3]-2*(x[4]+x[5]+x[6])+3*x[7]

fun.vals <- apply(x.vals,1, function(z) f(z))

minidx <- which.min(fun.vals)
fun.vals[minidx] 
x.vals[minidx,]
f(x.vals[minidx,])

Berend Hasselman