When directed by a vote of the resident taxpayers, as provided in Section 15-7 of this title, the county commissioners shall at their first meeting thereafter, notify the officers of the stock show or fair association named in the petition that the premiums shall be allowed and paid to the amount named in the petition and no more, provided, that admittance is free at all times to the stock show or fair association at which the premiums are offered. The commissioners shall determine and notify the association of the number and amount of premiums to be offered and have a premium list printed, which shall be furnished free to all interested. The premiums shall be paid in accordance with the list.