What is the reasoning for making a buddhist statue out of gold?

Practically, religious images are made using precious medals to prevent decay, so that the image can be available to venerate for many generations to come. From a more devotional aspect, choosing materials that we think of as beautiful shows a great reverence for the person that image represents. Religious images often "open and lift our minds" to higher ideals, including dharma practice, which is why, for example, people can be better practiticioners just by being in the temple's main hall, where the main images usually are.

I suppose a good analogy is showing respect for your boss and co-workers by coming to work in what best represents the workplace's business casual dress code, not just in a T-shirt with holes. Or, having enough respect for yourself to attend to your basic hygiene before leaving your home.

Precious metals and stones are frequently used in religious imagery. For example, in the Larger Pureland Sutra (Verse 54), we have:

Furthermore, throughout that land are trees made of the seven gems. There are trees of gold; trees of silver; trees of coral; trees of amber; trees of agate; trees of ruby; and trees of lapis lazuli. Then there are trees of two precious substances, trees of three, four, up to all seven.

Some gold trees have silver leaves, flowers and fruits. Some silver trees have gold leaves, flowers and fruits. Some coral trees have leaves flowers and fruit of amber. Some amber trees have leaves flowers and fruit of coral. Some agate trees have leaves, flowers and fruit of ruby. Some ruby trees have leaves, flowers and fruits of agate. Some lapis lazuli trees have leaves, flowers and fruit of all sorts of jewels.

There are trees with red gold roots, white silver trunks, coral branches, amber twigs, agate leaves, ruby flowers and lapis lazuli fruits. There are trees with white silver roots, coral trunks, amber branches, agate twigs, ruby leaves, lapis lazuli flowers and red gold fruit. There are trees with coral roots, amber trunks, agate branches, ruby twigs, lapis lazuli leaves, red gold flowers and white silver fruit. There are trees with amber roots, agate trunks, ruby branches, lapis lazuli twigs, gold leaves, silver flowers and coral fruits. There are trees with agate roots, ruby trunks, lapis lazuli branches, gold twigs, silver leaves, coral flowers and amber fruit. There are trees with ruby roots, lapis lazuli trunks, gold branches, silver twigs, coral leaves, amber flowers and agate fruit. There are trees with lapis lazuli roots, gold trunks, silver branches, coral twigs, amber leaves, agate flowers and ruby fruits.

The general understanding is that even the most beautiful objects we have on earth still pale in comparison to the beauty of the dharma, and this is just our feeble attempt to reflect that, and, like Jyothi said, offer our best to the Supreme One, who gives us a much more valuable gift.

Edit - user70 clarified:

What is the justification for such a statue? By justification I mean, what reasons would the Buddhists who created/use the statue give to explain why keeping gold (often seen as a sign of wealth and power) as a statue is right; as opposed to using the money from melting it down and selling it to buy meals for the homeless or others in need.

Well, a lot of institutions do both. At my Thai Forest (Theravdin) sangha, there are golden images, and we also give to charity, and obviously we do not charge for any services. The retreats, and even the Thai language classes, are completely donation-based. We do not shame anyone who cannot donate anything, and people with means donate more than enough to make-up for it. So we make sure that nothing keeps people from learning, not even lack of funds.

Not everyone will probably agree with this, but I propose that artistic beauty is an intrinsic good. This is why we continue to promote the arts in the secular world--I can't eat a beautiful painting, but it can nourish my mind, even if only in the moment I am looking at it. In my experience with working and feeding homeless people in a religious setting, many liked that we were providing them with food and warm shelter in the cold, as well as a beautiful setting to just appreciate our art. I don't know if many of us who have an almost unlimited access to beautiful images through internet searches can fathom living a life where all you saw was ugly, dark decay. It does not make for a healthy mind, which goes hand-in-hand with a healthy body.

So to answer your question, in the real world, it does not have to be an either/or decision (between beauty/charity), nor is it a zero-sum game where charity is sacrificed for art. When there are greedy people heaping up image after image for greed's sake, perverting the purpose of Buddhist imagery--which is to communicate the dharma--there should be accountability. The presence of art wouldn't hinder the advocacy of accountability.