To estimate the impact of proposed tax changes, the U.S. Department of the Treasury8 maintains two data files of records statistically characterizing the taxpayer population. Each of the i = 1,

c, 10,000 records in the first file represents a known number of families ai and describes corresponding characteristics such as family size and age distribution. Records j = 1,

c, 40,000 in the second file also represent a known number of families bj and contain some of the same characteristics as the first 1ai ai = ai bi2. However, most of the entries in the second file relate to the sources of income for family class j. To do a better job of analyzing proposals, the Treasury wants to merge these files into one with new records containing information drawn from both inputs.

Each new record will represent a collection of families formed by matching some or all of those in population ai with some of all in bj. The quality of the similarity between classes i of the first file and j of the second can be described by a distance measure di,j, and the Treasury seeks a minimum total distance merge. Explain how this problem can be modeled as a transportation problem by identify sources, sinks, supplies, demands, and costs. Also, explain how an optimal flow can be understood as a merge.