Welfare department may receive payment from patient or inmate of institution

institution. If any inmate or patient of any institution operated under the provisions of KRS 83.570, except the city workhouse, who is eligible for admission to said institution under the ordinances of the city and rules and regulations of the city's department of public welfare is financially able to pay a portion of the cost of his care, the city's department of public welfare shall have the authority to receive such payment as he is able to make.