Transformation Function In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (p.135):

$\begin{cases}Max\text{ }p*y\\s.t.\text{ }F(y)\leq0\end{cases}$

Where y is production vector and F(.) is a transformation function. 

The only information I have found about this function states that $F:R^L\to R$ and that production set of a firm could be represented as $Y=\{y\in R^L:F(y)\leq0\}$. Also if $F(y)=0$ it is named transformation frontier (p.562)

So I am interested in what concrete are these transformation function and transformation frontier. Intuitively it must be related to some feasibility restrictions but I whant to have some full and strickt explanation.

Will be very greatfull for help!
I know that this is an old question, but I thought I'd add an answer in case it's helpful to others with a similar question. My interpretation of the original question was that the question asker was looking for a concrete example of how a production function and a transformation function might be related. So I am providing a simple example. 

Suppose we have a firm that produces a single output, $ q$, using a Cobb-Douglas production function of the following form: 

$$ q\le f(x_1,x_2)=x_1^\alpha x_2^\beta $$

That is, $ f(x_1,x_2) $ describes the maximum amount of $ q$ that can be produced by a firm with this technology. So the production possibilities set, $ \mathbf Y$, is the set of all vectors $ \mathbf y=(-x_1,-x_2,q), \mathbf y\subseteq \mathbb R^3 $ (in this case - clearly could be extended to $ \mathbb R^n $), such that the inequality above holds. 

$$ \mathbf Y=\{\mathbf y|q\le f(x_1,x_2)\} $$

Note that the vector has negative signs on $ x_1$ and $ x_2$ because they are inputs, while the output, $ q$, is positive. 

An equivalent way to represent this is as a transformation function, $ F: \mathbb R^3 \to \mathbb R$, where 

$$ F(\mathbf y) = q-x_1^\alpha x_2^\beta $$

Using this notation, 

$$ \mathbf Y=\{\mathbf y|F(\mathbf y) \le 0 \} $$

Where $ F(\mathbf y) \le 0 $ implies that the first inequality is satisfied. 

This is fairly simple to interpret when there is only one output; however the concept of a transformation function is useful because it allows us to think about production technologies that might use multiple inputs and produce multiple outputs. 

I hope this is useful!