Jsun Yui Wong
The computer program listed below seeks to solve the following problem in Abdel-Baset and Hezam [1, p. 87, Test Problem 10]:
Maximize ((13 * X(1) + 13 * X(2) + 13) / (37 * X(1) + 73 * X(2) + 13)) ^ -1.4 * ((64 * X(1) - 18 * X(2) + 39) / (13 * X(1) + 26 * X(2) + 13)) ^ 1.2 - ((X(1) + 2 * X(2) + 5 * X(3) + 50) / (X(1) + 5 * X(2) + 5 * X(3) + 50)) ^ .5 * ((X(1) + 2 * X(2) + 4 * X(3) + 50) / (5 * X(2) + 4 * X(3) + 50)) ^ 1.1
subject to
2*X(1) + X(2)+ 5*X(3)<=10,
5* X(1) -3* X(2) =3,
1.5 <= X(1) <= 3,
X(1) >=0,
X(2) >=0,
X(3) >=0,
X(4) below is an added slack variable.
The following computer program is very similar to the computer program of the preceding paper. One notes the following line 193, line 194, and line 209.
0 DEFDBL A-Z
2 DEFINT K
3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)
12 FOR JJJJ = -32000 TO 32000 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
70 FOR J44 = 1 TO 3
72 A(J44) = RND * 10
73 NEXT J44
128 FOR I = 1 TO 500
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 2))
181 J = 1 + FIX(RND * 3)
183 r = (1 - RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
193 REM X(2) = INT(X(2))
194 REM X(3) = INT(X(3))
196 X(1) = ((3 + 3 * X(2)) / 5)
201 IF X(1) < 1.5 THEN 1670
203 IF X(1) > 3 THEN 1670
205 FOR J44 = 1 TO 3
206 IF X(J44) < 0 THEN 1670
208 NEXT J44
209 REM IF X(1) = ((3 + 3 * X(2)) / 5) THEN 311 ELSE GOTO 1670
311 X(4) = 10 - 2 * X(1) - X(2) - 5 * X(3)
333 FOR J44 = 4 TO 4
336 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
339 NEXT J44
368 POBA = ((13 * X(1) + 13 * X(2) + 13) / (37 * X(1) + 73 * X(2) + 13)) ^ -1.4 * ((64 * X(1) - 18 * X(2) + 39) / (13 * X(1) + 26 * X(2) + 13)) ^ 1.2 - ((X(1) + 2 * X(2) + 5 * X(3) + 50) / (X(1) + 5 * X(2) + 5 * X(3) + 50)) ^ .5 * ((X(1) + 2 * X(2) + 4 * X(3) + 50) / (5 * X(2) + 4 * X(3) + 50)) ^ 1.1 + 1000000 * (X(4))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 4
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -11111 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4)
1912 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [35]. The complete output through JJJJ = -31999.95000000001 is shown below:
1.499999940486506 1.499999900810843 3.250025687713525D-15
0
8.279865664817091 -32000
1.499999940436654 1.499999900727757 2.933276876528936D-14
0
8.279865664927954 -31999.99
1.499999940494236 1.499999900823726 5.694494383392632D-16
0
8.2798656647999 -31999.98
1.49999994040392 1.4999999006732 9.525181472646168D-16
0
8.27986566500075 -31999.97000000001
1.499999940563297 1.49999990093883 1.126725673329401D-15
0
8.279865664646318 -31999.96000000001
1.499999940400582 1.499999900667637 1.475714966596027D-14
0
8.27986566500817 -31999.95000000001
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [35], the wall-clock time for obtaining the output through
JJJJ= -31999.95000000001 was two seconds, not including the time for "Creating .EXE file." One can compare the computational results above to the results in Abdel-Baset and Hezam [1, p. 88, Table 1].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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