The work of constructing, equipping, and furnishing the building shall be conducted and completed under the direction and supervision of the commission. The commission members are charged with the duty of requiring that the work is done in accordance with the plans and specifications. The commission may employ architects, engineers, supervisors, inspectors, clerks, and other employees to supervise and inspect the work and assist in the performance of the duties of the commission. The county and city shall pay the fees and salaries of the employees in the amounts fixed by the commission, one-half by the county and one-half by the city, when presented with statements certified to be correct by a majority of the commission. The employment is subject to the approval of the city council and county board in the manner provided in this chapter.