Whenever land, upon which is located the bed of such a mapped street or public drainageway, flood control basin or public area reserved in the Official Map, cannot yield a reasonable return to the owner unless a building permit is granted, the Land Use Board may, in a specific case, by an affirmative vote of a majority of the full authorized membership of the Board, direct the issuance of a permit for a building or structure thereon in such manner as will minimize the increase of the cost of opening such street or cause a minimum change of the Official Map; and the Board shall impose reasonable requirements to protect the public health, morals, safety and general welfare as a condition of approval.