Table 1 below

Table 2 below

Table 3 below

Problem 18-11 One operator services a bank of five machines. Machine running time and service time are both exponential. Machines run for an average of 90 minutes between service requirements, and service time averages 35 minutes. The operator receives $20 per hour in salary and fringe benefits, and machine downtime costs $70 per hour per machine. Use Table 1, Table 2 and Table 3. a. If each machine produces 60 pieces per hour while running, find the average hourly output of each machine, when waiting and service times are taken into account. (Round your answer to 2 decimal places.) Average hourly output pieces X M D F X M D F X M D F X MDF TABLE 18.7 Finite-queuing tables Population 5 .125 2 .082.994.260 3.058 994 440 3238 960 .012 1.060 999 1.575.920 2 303 950 2.652 807 .0191 .095 998 .130 2 .089.933 1 .903.695 1 .992 .451 .0251 .125 997 1 594 914 270 3.064.9944604 .045 995 .030 1 .149.996.135 2 .095.933 2 323.944 3 .266 953 .034 1 .169 .995 1 .612.907 1 .915.677 2.686 787 .036 1 179 .994.140 2.102.992.280 3 .071.993 1994.432 .040 1 .199 993 1 .630.900 2 342.938.480 4 .053.994 .042 1 .208 992 .145 3 .011 .999 1 .925 .661 3 296.945 .044 1 .218 991 2 .109.991.2904 .007 .999 2 719 767 .046 1 .228 990 1 .647.892 3.079.992 1 .996 415 .050 1 .247 989 .150 3 .012999 2 362.932.500 4.063 992 .0521 .257 .988 2 .115.990 1 934 .644 3 327 936 .054 1 .266 987 1 664 885 .300 4.008 .999 2 .750 748 .056 2 .018 999.155 3 .013 .999 3 .086 .990 1 .997.399 1 276985 2.123.989 2.382 926 520 4.073 991 2058 2 .019 999 1 .680 877 1 .942.628 3 .359.927 1 .285.984.160 3 .015999 310 4 .009 .999 2 779 728 .0602 .020 999 2 .130 988 3.094 989 1 .998 384 1 .295 983 1.695.869 2.402.919.540 4 .085.989 .062 2 .022.999.1653 .016 999 1 950.613 3.392.917 1 304 982 2.137.987.320 4 .010 .999 2.806 708 ,064 2 .023 999 1 .710 861 3 103.988 1 .998 370 1 .314.981.170 3 .017 .999 2.422 912 560 4.098 986 .066 2 .024 999 2 .145.985 1 956 597 3 426 906 1 323 979 1 .725.853 330 4 .012.999 2.831.689 .068 2 .026 999.180 3 .021.999 3.112.986 1 999 357 1 333 978 2 .161.983 2 .442.904.580 4 .113 984 .070 2 .027 999 1 .752.836 1 .962583 3 461 895 1 .342 977.190 3 .024 998.340 4 .013 .999 2 .854.670 .075 2 .031 .999 2 .117 980 3.121.985 1 .999.345 1 1 365 973 1 1 .778 819 2 .462.896.600 4.130 981 .080 2 .035 998 200 3 .028 998 1 .967 569 3 497 883 1 388 969 2 .194.976 380 4.017 .998 2.875 652 .085 2 .040 998 1 .801 801 3 .141 .981 1 999 353 1 .410 965 .210 3 .032.998 2 501 .880.650 4.179.972 .090 2 .044 998 2 2 .211 973 1 975 542 3 588 850 1 .432 .960 1 .822 783 380 4 .021.998 2 918 608 .0952 .049 997 .220 3 .036.997 3.163.976 1 .999 .308 1 .454 955 2 .229.969 2 540.863.700 4 .240.960 .100 2 .054 997 1 .842 765 1 .981 516 3.678 815 1 .475 950 .2303 .041 .997.400 4.026.997 2.950.568 .1052 .059.997 2 .247 .965 3.186.972 1 999 286 1 496 945 1 .860 747 2 579.845.750 4 316 944 .110 2 .065 996 .240 3 .046 996 1 .986 493 3 .763 777 1 .516 939 2 .265.960.420 4.031.997 2.972.532 .1152 .017 995 1 .876 730 3 211.966.800 4 410 924 1 .537 933 .250 3 .052.995 2 .616.826 3 841 739 .1202 .076 995 2 .284.955 1 989 471 2 987 .500 1 .556 .927 1 .890 712.440 4 .037996 (continued) X MD FX M D Fx M D F X MDF .135 2 .064 .066 1 2 5 4 1 1 .140 4 3 .068 3 .900 .702 .470 .871 .666 444 .838 .631 3 2 2 .415 .907 .028 .132 437 .919 .032 .144 .460 .929 1 1 2 1 5 4 3 .070 .145 4 3 2 3 1 .940 .995 .936 .999 .994 .931 .999 .994 .926 .999 .992 .913 .999 .990 .899 .999 .988 2 2 .075 1 1 3 2 ,019 .952 .220 .699 .999 .991 .947 .680 .230 .999 .990 .941 .662 .240 .989 .935 .644 .998 .987 .250 .928 .627 .998 .986 .150 .036 .998 5 .997 4 3 1 4 .080 3 2 3 2 2 1 1 4 .155 1 547 .126 .562 .020 .133 .577 .022 .140 .591 .026 .158 .627 .031 .177 .660 .037 .196 .692 .043 .216 .722 .049 .237 .750 .056 .258 .776 .064 .279 .800 .085 3 3 .997 .996 .995 .994 .993 .992 .991 .990 .999 .988 .999 .986 .999 .984 .999 .982 .156 .483 .939 .040 .169 .505 .947 .044 .182 6 2 2 5 4 .032 1 .883 1 .090 3 .160 4 3 2 3 2 1 2 .528 1 .095 3 .998 .986 .867 .998 .984 .850 .998 1 .921 .610 .997 .260 6 2 .165 4 5 .954 .049 .195 .550 3 1 3 .984 .914 .100 .850 4 .522 3 .907 2 .995 .900 4 .656 3 .957 2 .998 .950 4 .815 3 .989 Population 10 .016 1 .144 .170 .021 1 .188 .023 1 .206 .025 1 .224 026 1 .232 028 1 .250 .030 1 .268 2 .053 1 .285 .034 2 .037 1 .301 .036 2 .041 1 .320 .038 2 .046 1 .337 2 .050 1 .354 .042 2 .055 1 371 .044 2 .060 1 .046 2 .065 1 404 .048 2 .071 1 421 .050 2 .076 1 .437 .052 2 .082 1 .054 2 .088 1 .470 .056 2 1 486 .058 2. .100 .501 .060 2 .106 1 .517 .062 2 .113 1 .532 ,064 2 .119 2 4 3 2 1 .030.998 .124 990 366 .954 .761 .815 .993 453 .037 .998 .142 .988 .400 .947 .791 .794 .995 434 .044 .162 .986 .434 .908 .819 774 .996 .416 .010 .999 .052 .997 .183 .983 .469 .929 .844 .753 .997 .400 2013 .999 .060.996 .205 .980 .503 .919 .866 732 .998 .384 .015 .999 .070 .228 .976 .537 .908 .886 712 .999 .370 .018 .999 .081 .994 .252 .972 .571 .896 .903 .692 .999 .357 .022 .999 .093 .995 .278 .968 .603 .884 .918 .672 .999 .026 .998 .106 .991 .304 .963 .872 .040 .999 2 .981 1961 .594 1 4 .170 1 3 .105 3 .270 6 .980 .999 .978 .998 .054 .209 .571 .966 .995 2 1 3 2 1 5 5 4 3 .388 .975 .110 ,072 .180 .013 4 2 .066 .238 3 1 2 1 3 2 .115 2 .280 6 .301 .822 .081 .324 .843 .016 .090 1 5 .614 .975 .016 5 4 .997 .982 .906 .579 .999 .996 .978 .890 .890 .999 .995 .973 .873 .522 .999 .994 .968 .854 1 .190 .120 4 4 3 3 3 2. .832 .997 .978 .814 .997 .974 .795 .996 .971 .776 .999 .995 .967 .756 .999 .994 .962 .737 .999 .994 .958 .718 .999 .993 .454 2 346 .998 .973 .998 .970 .998 .967 .997 .963 .997 .960 .997 .956 .996 953 .996 1949 .996 .945 .995 1 .290 1 6 5 4 .125 4 2 1 5 4 3 .200 .094 3 3 2 1 4 3 .078 .269 .654 .982 .020 .092 .300 .692 .987 .025 .108 333 .728 .990 .861 .019 .100 369 .878 .022 .110 .392 .893 .025 .121 .130 2 1 5 .497 2 1 6 .345 .210 .300 4 3 2 1 4 3 .999 .992 .961 .835 .474 5 4 3 .135 ,635 2 1 (continued) X MD FX M D FX MD FX MDF .300 N 6 5 4 3 .310 3 2 8 7 6 7 6 5 4 3 2 7 5 9 6 4 8 1 6 5 4 3 2 6 5 4 3 2 6 320 5 4 3 3 2 8 7 6 5 4 2 7 6 7 6 5 9 .330 8 5 5 4 7 4 3 6 3 5 4 3 2 7 4 2 8 .932.653.400 .999 353 .031.998 .120.990 .331 .957 .666 858 420 .943.635 .036 .998 .135.988 359.952 .695.845 .952.617 440 .042.997 .151.986 .387 .945 .723 831 .961 .600 .010 .999 460 .049.997 .168 .983 .416 .938 .750.816 .968 584 2014 .999 .064 .995.480 .205.978 .474.923 .798 787 .978 553 .019 .999 .083.996 .247.971 .500 .533 .906 .840 .758 .986 525 .026 .998 .340 .105.991 .500 .292.963 .591 .887.520 .875 .728 .991 499 .034 .993 .130 .987 341 .954 .646.866 .905 700 .540 .994 .476 .045 997 .160 .984 .392 .943 .698 .845 .928 .672 .560 .996 454 .011 .999 .058.995 .193 .979 445 .930 .747 .822 .580 .947 .646 .998 435 .015.999 .074 .994 .230 .973 .499 .916 .600 .791 .961 .621 .998 .417 .020 .999 .093 .992 .271 .966 .553 .901.650 .830 775 8 7 6 5 .972 .598.650 .999 400 .026 998 .115 .989 .316 .958 .606 .884.700 .864 .752 .980 575 .999 385 .034 .997 .141 .986 .363 .949.750 .658 .867 .893 .729 .986 .555 .044 .996 .171 .982 413 .939 .800 .707 .848 .917 .706 .991 .535 .057 .995 .204 .977 .465 .927 .850 .753 .829 .937 .684 .994 517 .010 .999 .072.994.900 .242 .972 .518 .915 .795 .809 .953 .663 .950 .996 .500 .021 .999 .123 .988 .353.954 .651.878 .882.759 .980.614 .999461 .040.997 .200 .979 .484 .929 .772.836 .940 .711 .992.571 .075 994 .307.965 .626 897 .870.792 .975.666 .998.533 .134.988 .446.944 .763.859 .939.747 .991.625 .999.500 .232.979 .611 .916 .879 .818 .978 705 .998 .588 387.963 .785 881 .957.777 .995.667 .630.938 .934 841 .994 737 9 8 7 7 6 4 5 3 6 5 4 8 7 4 360 6 9 6 5 4 3 2 7 6 5 4 3 2 7 6 3 2 8 7 6 5 4 3 8 7 6 .799 .380 5 4 3 9 8 7 6 5 4 3 9 8 2 Noo o o o o o on 5 4 8 7 3 2 7 6 5 4 .400 Source:L. G. Pack and R. N. Hazelwood, Finite Queuing Tables New York: John Wiley & Sons, 1958). Reprinted by permission