Optimizing

Hey,

It's actually not homework, what gave you that impression?

I graduated in
May and studied Math, economics, and international relations, so I don't
have much of a programming background.  This is a project that I'm working
on out of personal interest.

Obviously, I've tried doing some homework, but after 45 minutes of digging
around without even really having any leads I figured I would post here.

The optimization problems I see more generally seem tailored towards
maximizing a function subject to some constraint on that function.  For
example, maximizing U(x,y)=2x^2+4y s.t. x+y=3.  I don't really see a way to
frame my current maximization like that at all.  We aren't choosing one
observation in our dataset, we are choosing a group.  And, the constraints
aren't something like the types sum to a number, but rather that our choice
of observations meet some specific condition.

Sorry if I'm being clueless here, but when I look at
http://cran.r-project.org/web/views/Optimization.html I just see a giant
list of packages, most of which I believe are optimizing a function subject
to constraints.  Maybe my problem actually is a common one, there is some
package out there that would do it, and I just need to find it.  If so, my
googling and looking on the help pages has been so far unsuccessful. I
apologize if the answer really is sitting there on some help page, but I
really haven't found it.  If this were some homework problem, then I would
know that it's probably a common, normal thing, and feel more confident
looking on the Cran page.  But, since it isn't, I wasn't even sure if the
answer was out there and my searching had so far been fruitless.  That's
why I wanted to know if there would be some function that would do this
sort of thing or if it's the sort of thing that I just need to manually
work through.

The help pages are over my head in so far as the help pages are highly
technical and focused on methods.  They assume a knowledge about the basic
type of optimization problem that I don't have, and I think that's because
there is a standard type of optimization that is most common.

Anyways, I am thinking I might just try to manually do the calculation
because I can't follow the optimize commands.  The general strategy I think
is to somehow make a dataset that has all combinations of 6 people as rows.
 Then, for each row, make a vector that is just all the types of the people
in that row, a vector for the sum of the values, and a vector for the sum
of the wages.  Then, keep only those rows which have the correct types and
wages under the max.  Then, sort by the sum of the values.  Let me know if
you have any better ideas!

Sam


On Wed, Nov 14, 2012 at 7:35 PM, Bert Gunter <gunter.berton at gene.com> wrote:

Sam:

1. Homework? R has a no homework policy.

2. But in any case, check out the Optimization task view on CRAN. You
should be able to find something there that meets your needs.

Of course, if something is "a little over your head," that's not an
excuse, but rather an admission that you have to do some "homework" on
your own.

Cheers,
Bert

On Wed, Nov 14, 2012 at 5:23 PM, Sam Asin <asin.sam at gmail.com> wrote:

Hello,

I am fairly new with R and am having trouble finding an optimal group.  I
checked the help functions for the various optimize commands and it was a
little over my head.

I have a dataset with 4 columns, name, type, value, and cost.  The set
consists of a list of people, which have 3 types.  I want to choose 6
people, two of each type, and maximize the sum of their values.  However,
I'm subject to the constraint that the wage of the three people has to

sum

to less than 20 dollars.  Here is some sample data.

people <- c("A", "B", "C", "D", "E", "F", "G", "H", "I")
type<- c(1, 1, 1, 1, 2, 2, 3, 3, 3)
value<-c(25.20, 24, 38, 20, 14, 20, 31, 11, 8)
wage<- c(4, 3.8, 5.1, 3.5, 2.4, 3, 6, 2.4, 2)

data<- data.frame(people, type, value, wage)

With this small dataset the question isn't very interesting, but the

answer

would be something like person C, D, E, F, G, and I (I didn't check to

see

that those prices sum to less than $20).

How can I write a program that will do this?  Can I just use the optimize
command?  Do I have to transform my dataset into something that is easier
to use the optimize command on?  Or should I write my own code that does
the process?

Thanks,

Sam

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