Vol. 10 No 5 - Pi Mu Epsilon

PROBLEMS AND SOLUTIONS 429868. [Fall 19951 Proposed by William H. Peirce, Delray Beach,Florida.1. Enter total amount of all social securitybenefits . . . . . . . . . . . . . . , . .2. Enter one-half of line 1 . . . . . 2.7. Enter your provisional income . . . . . 7.-p-8. Enter $32,000 if married filing jointly 8.32,000-9. Subtract line 8 from line 7. If zero orless, enter 0 . . . . . . . . . . . . . . . . . . 9.Is line 9 zero? If yes, enter 0 on line 18. Ifno, continue to line 10.10. Enter $12,000 if married filing jointly 10.12,000-11. Subtract line 10 from line 9. If zero orless, enter 0 . . . . . . . . . . . .. . . . . . 11.12. Enter the smaller of line 9 or line 10 12.13. Enter one-half of line 12 . . . . . . . 13.14. Enter the smaller of line 2 or line 13 14.15.Multiplyline11by0.85 ........ 15.16.Addlines14and15 .......... 16.17. Multiply line 1 by 0.85 . . . . . . . . 17.18. Taxable social security benefits. Enterthe smaller of line 16 or l&e 17 . . . . . . 18. TSocial Security Benefits Worksheet (somewhat simplified)1.- S -Computation of the taxable portion of social security benefits in 1994is considerably more complicated than in past years, and the IRS hasdesigned the 1994 accompanying worksheet to determine these taxablebenefits. Let S be the total social security benefits on line 1, P theprovisional income on line 7, and T the taxable benefits on line 18. Formarried couples filing jointly, find T as a function of S and P. Exhibit thesolution graphically by showing the function T for each pertinent region ofthe SP-plane, and give the boundary equations for each region. Assume S> 0 and P > 32,000 and ignore their practical upper limits.Solution by Paul S. Bruckman, Salmiya, Kuwait.We consider the possibilities in the table below.Line-1.Value