Hi people,
Do you know a good source that reviews this topic in detail.
Thanks in advance.
The subject in question is known as Linear Programming/Optimization
I recommend Linear Programming and it's Applications by James K. Strayer. It covers the simplex algorithm which is the by far the simplest algorithm for solving such systems. Give you a great introduction to the field, along with Tableaus.
Strictly speaking you are correct, but since the $\displaystyle \Gamma(n+1) = n!$ for $\displaystyle n \in \mathbb{N} $. It's useful to use the gamma function to define the factorial function for non-integer reals.
I.e, $\displaystyle \frac{1}{2}! = \frac{\sqrt{\pi}}{2}$
So it is merely an extension of the factorial function. Many sources agree with me on this point.