Based on Glover and Klingman XXXXXXXXXXThe government has many computer files that must be merged frequently. For example, consider the Survey of 5.7 Conclusion 277 Current Income (SCI) and the...

Based on Glover and Klingman (1977). The government has many computer files that must be merged frequently. For example, consider the Survey of 5.7 Conclusion 277 Current Income (SCI) and the Consumer Price Service (CPS) files, which keep track of family income and family size. The breakdown of records in each file is given in the file P05_69.xlsx. SCI and CPS files contain other pieces of data, but the only variables common to the two files are income and family size. Suppose that the SCI and CPS files must be merged to create a file that will be used for an important analysis of government policy. How should the files be merged? We would like to lose as little information as possible in merging the records. For example, merging an SCI record for a family with income $25,000 and family size 2 with a CPS record for a family with income $26,000 and family size 2 results in a smaller loss of information than if an SCI record for a family with income $25,000 and family size 2 is merged with a CPS record for a family with income $29,000 and family size 3. Let the “cost” of merging an SCI record with a
 I_SCI
and I_CPS
are the incomes from the SCI and CPS records, and FS_SCI
and FS_CPS
are the family sizes. Determine the least expensive way to merge the SCI and CPS records.