Recursive(?) algorithm design

A dangerously easy, and your-situation-specific well-performable solution!

<?php
class solver {
    private
            // The final output array
            $arr_evaled,
            // When a cell gains its final value, the corresponding entry in the following array gets marked as being done!
            $arr_done;

    private $solving_iterations_count;

    public function solver($array) {
        $this->arr_done = array();

        foreach($array as $k => $arr)
            $this->arr_done[$k] = array('Quantity' => false, 'Value' => false);

        // Firstly,expand all of the "[x]Cost"s to "([x]Quantity*[x]Value)"s!
        $this->arr_evaled = array_map(
            function($v){ return preg_replace('#\[(\d*?)\]Cost#', '([$1]Quantity*[$1]Value)', $v); },
            $array
        );

        $this->solving_iterations_count = 0;
        $this->solve();
    }

    private function isDone() {
        foreach($this->arr_done as $a)
            if($a['Quantity'] == false || $a['Value'] == false)
                return false;
        return true;
    }
    private function isCellDone($id, $fieldName) {
        return $this->arr_done[$id][$fieldName];
    }
    private function markCellAsDone($id, $fieldName, $evaluation) {
        $this->arr_done[$id][$fieldName] = true;
        $this->arr_evaled[$id][$fieldName] = $evaluation;
    }
    private function isEvaluable($str) {
        return preg_match('#^[0-9*+-\/\(\)\.]*$#', $str) == 1 || strtolower($str)=='null';
    }
    private function replace($from, $to) {
        foreach($this->arr_evaled as &$arr) {
            $arr['Quantity'] = str_replace($from, $to, $arr['Quantity']);
            $arr['Value'] = str_replace($from, $to, $arr['Value']);
        }
    }

    private function solve() {
        $isSolvable = true; // YOUR TODO: I believe coding this part is also fun!) (e.g: check for "reference cycles")
        if(!$isSolvable) return null;

        while( !$this->isDone() )
        {
            foreach($this->arr_evaled as $arr) {
                foreach(['Quantity', 'Value'] as $fieldName) {
                    if(!$this->isCellDone($arr['id'], $fieldName)) {
                        if($this->isEvaluable($arr[$fieldName])) {
                            $evaluation = eval("return {$arr[$fieldName]};");
                            $this->markCellAsDone($arr['id'], $fieldName, $evaluation);
                            $this->replace("[{$arr['id']}]$fieldName", "$evaluation");
                        }
                    }
                }
            }
            $this->solving_iterations_count++;
        }
        foreach($this->arr_evaled as &$row)
            $row['Cost'] = $row['Quantity'] * $row['Value'];
        return $this->arr_evaled;
    }

    public function print_tabulated() {
        echo "The count of solving iterations: {$this->solving_iterations_count}<br/><br/>";
        echo '<table border="1"><tr><th>id</th><th>Name</th><th>Quantity</th><th>Value</th><th>Cost</th></tr>';
        foreach($this->arr_evaled as $arr)
            echo "<tr><td>{$arr['id']}</td><td>{$arr['Name']}</td><td>{$arr['Quantity']}</td><td>{$arr['Value']}</td><td>{$arr['Cost']}</td></tr>";
        echo '</table>';
    }
}

// Testing
$arr = array(
    1 => array( 'id' => 1, 'Name' => 'Regulating', 'Quantity' => '[2]Quantity+[3]Value', 'Value' => '[2]Cost'  ),
    2 => array( 'id' => 2, 'Name' => 'Kerbs',      'Quantity' => '3',                    'Value' => '6'        ),
    3 => array( 'id' => 3, 'Name' => 'Bricks',     'Quantity' => '9',                    'Value' => '7'        ),
    4 => array( 'id' => 4, 'Name' => 'Sausages',   'Quantity' => '[3]Cost',              'Value' => '3'        ),
    5 => array( 'id' => 5, 'Name' => 'Bamboo',     'Quantity' => '[4]Quantity',          'Value' => '[7]Cost'  ),
    6 => array( 'id' => 6, 'Name' => 'Clams',      'Quantity' => '[4]Quantity',          'Value' => 'NULL'     ),
    7 => array( 'id' => 7, 'Name' => 'Hardcore',   'Quantity' => '[3]Quantity*0.5',      'Value' => '12'       ),
    8 => array( 'id' => 8, 'Name' => 'Beetles',    'Quantity' => '[6]Quantity*[4]Value', 'Value' => '[2]Value' ),
);
echo '<pre>';
(new solver($arr))->print_tabulated();

Here is the output: