All individuals admitted to a state institution operated by the department of developmental disabilities under section 5123.03 of the Revised Code shall be maintained at the expense of the state. Their traveling and incidental expenses in conveying them to the state institution shall be paid by the county of commitment. Upon admission, the individuals shall be neatly and comfortably clothed. Thereafter, the expense of necessary clothing shall be borne by the responsible relatives or guardian if they are financially able. If not furnished, the state shall bear the expense. Any required traveling expense after admission to the state institution shall be borne by the state if the responsible relatives or guardian are unable to do so.