There is hereby created the Legislative Budget and Finance Committee which shall consist of the President pro Tempore of the Senate and five other members of the Senate, the Speaker of the House of Representatives and five other members of the House. The President Pro Tempore of the Senate shall appoint the Majority Leader of the Senate, the Minority Leader of the Senate and three additional members of the Senate. Two of the three additional members shall be members of the Minority Party. The President Pro Tempore of the Senate, the Majority Leader and the Minority Leader may designate other members of the Senate to be appointed in their stead. The Speaker of the House of Representatives shall appoint the Majority Leader of the House of Representatives, the Minority Leader of the House of Representatives and three additional members of the House. Two of the three additional members shall be members of the Minority Party. The Speaker of the House, the Majority Leader and the Minority Leader may designate other members of the House to be appointed in their stead. Members of the committee shall be appointed or reappointed during each regular session of the General Assembly, and shall continue as members until the first Tuesday in January of the next odd-numbered year and until their respective successors shall be appointed, provided they continue to be members of the Senate or the House of Representatives. The term of office of such committee members as shall not continue to be members of the Senate or the House of Representatives shall cease upon the convening of the next regular session of the Legislature after their appointment. The committee has a continuing existence and may meet and conduct its business at any place within the Commonwealth during the sessions of Legislature or any recess thereof and in the interim between sessions.