When the department determines that a patient is unable to pay the entire cost determined pursuant to section 83-365, the department shall then determine the ability of his relatives to pay such cost. In making this determination, the department shall consider the relative’s taxable income reportable under Nebraska law, and the patient’s length of care and treatment. At the request of the relative, the department also shall consider other relevant factors in the interest of avoiding undue hardship. Such factors may include the relative’s age, provision for his retirement years, his assets, his liabilities, the number of his dependents, and their mental and physical condition and educational requirements.