The department of mental health and addiction services shall charge a patient, patient’s estate, or liable relative an amount discounted from the amount the department charges under section 5121.33 of the Revised Code if the department determines through the application process described in section 5121.36 of the Revised Code or through the financial assessment process described in section 5121.37 of the Revised Code that the patient, estate, or relative is eligible for a discount.