A medicine is administered to a patient and t hours later the blood concentration of the active ingredient is given by $c ( t ) = t e ^ { - t / 2 }$ milligrams per milliliter. Determine the maximum value of $c ( t )$ and indicate at what moment this maximum value is reached. Knowing that the maximum safe concentration is $1 \mathrm { mg } / \mathrm { ml }$, indicate whether there is risk to the patient at any time.