The Council shall serve as the Zoning Board of Adjustment and may authorize a variance from these regulations when, in its opinion, undue hardship will result from requiring strict compliance. In granting a variance, the Council shall prescribe only conditions that it deems necessary to or desirable in the public interest. In making the findings hereinbelow required, the Council shall take into account the nature of the proposed use of the land involved, existing uses of land in the vicinity, the number of persons who will reside or work in the proposed use, and the probable effect [of] the variance upon traffic conditions and upon the public health, safety, convenience and welfare in the vicinity.