Optimum markup by direct solution

A direct solution technique determines optimum markup for competitive construction bids using either lowest opposing bid models or average opposing bid models. A graphical representation helps explain the technique. Lowest competing bids can be standardized, and a table shows standardized optimum markup to fit any normally distributed lowest opposing bids. The paper explains: (1) the effects of differing numbers of competitors on the lowest opposing bids; and (2) the relationship between average and lowest opposing bids for differing numbers of competitors. The direct method provides the same answers as an accurate trial-and-error method, but it is quicker, once the variables of a normal distribution are calculated. Its quickness leads to easy comparisons for numbers of competitors.