Feature/add solution class

[MWL91]

#9 I've created (in my opinion) clearer way to product linear program.
Now it all may be written as a one class, and from that class you may take answers.

Using LinearProgram class

Using \Simplex\Formulation\LinearProgram you can formulate linear program solution.

For example let's assume, that we have given linear problem:

z = 2x1 + x2

with constraints:

x1 + x2 >= 2

x1 - x2 = 0

x1 - x2 >= -4

that we can describe in following way:

use \Simplex\Formulation\LinearProgram;
use \Simplex\Formulation\Formula;
use \Simplex\Formulation\GreaterOrEqual;
use \Simplex\Formulation\Equal;

$program = new LinearProgram(
    new Formula(2, 1),
    [
        new GreaterOrEqual(new Formula(1, 1), 2), 
        new Equal(new Formula(1, -1), 0), 
        new GreaterOrEqual(new Formula(1, -2), -4),
    ]
);

Now we can take maximum solution with only:

$program->getMax(); // return 12

And optimized parameters:

$solution = $program->getSolutionFormula();
// returns new Formula(4, 4, 6, 0);

$solution->getParam('x1'); // 4
$solution->getParam(1); // the same as upper 4

[uestla]

@MWL91 Hello and sorry for reacting this late after your PR.

The library has gone through bigger refactoring lately and the core was rewritten to use bcmath for better precision. The API however stood the same, and some more helpful methods were added (including getSolution() and getSolutionValue() on the Solver class - which behaves practically the same as your getMax() method).

Anyway, I have to say I really like your API since it removes the variable naming ("x1, x2, ...") and adds more OOP-way of doing things. Vector of coefficients where index is the input variable is really clever. Also having multiple constraint classes for each type (GOE, LOE, EQUAL) is also much better approach.

I'll think about changing the API and maybe release new major version after that.

What I would like to keep however is the support for older PHP versions (even if they're already in EOL state).