Problem 18-10 (Static) Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentially distributed and has a mean of 14 minutes per machine. The machines operate for an average of 86 minutes between adjustments. While running, each machine can turn out 50 pleces per hour Use Table 1. Table 2 and Table 3 a. Find the probability that a machine will have to wait for an adjustment (Round your answer to 3 decimal places.) Probably 0.437 b. Find the average number of machines waiting for adjustment (Round your answer to 2 decimal places.) Average number of machine waiting 0.53 machines c. Find the average number of machines being serviced. (Round your answer to 2 decimal places.) 1.33 machines d. The expected hourly output of each machine, taking adjustments into account. (Round your answer to 2 decimal places.) Expected hourly output pieces e. Machine downtime represents a cost of $70 per hour operator cost (including salary and fringe benefits) is $15 per hour. What is the optimum number of operators? 1 operator O2 operators 3 operators eneratore 036 Lapier iochia table1.png X MD FX MD FX M D F X MD F TABLE 18.7 Population Finite-queuing tables .125 2 042 .900 200 3 012 1 .800 058.934440 2 1 2830 900 -575 .920 2 .019 303.950 2 1 382 095 998.130 2 089.833 1 .025 1 1 .125 .S03895 997 .982 A57 1 .994 .914 270 3 .030 064 .994 480 6 1 149 996 .135 045 995 2 095 .833 2 3z3.944 3 .034 1 .169 995 206 953 1 .612 .907 1 915 577 2 .179 994 .140 586 700 2 102 .992.280 3 .071.993 1 994 432 .040 .199 983 1 530 .900 2 342 938 480 4 053 934 042 1 .208 982 .145 3 011 .999 1 925 661 3 286 945 044 1 218 991 2 109 .991 280 4 .007 .999 2 719 767 016 1 228 990 1 1647 892 3 079992 1 996 415 050 1 .247 989 .150 3 .012999 2 362932.500 4 063 982 0521 .257 988 2 .115 .990 1 934 .844 3 327 966 .054 1 266 987 1 .885 300 4 008.999 2 750 748 058 2 2018 999 155 3 999 3 086 990 1 997 399 1 .276 985 Z .123 .989 2 382 926.520 4 073 981 058 2 019 999 1 580 .877 1 942 .628 3 359 927 1 285 984 .160 3 015 999 310 4 .009999 2 779 728 2 020 999 2 .130 .988 3 094 989 1 998 384 1 -295 963 1 .895 .869 2 402 919.540 4 085 989 .062 2 022 999.165 3 016 999 1 950 .613 3 392 917 1 304 982 2 .137 .987 320 4 010 999 2 806708 2 064 .023 999 1 710 861 3 1 .103 988 998 370 1 314 170 3 4 2 017 422 912.560 981 098386 066 2 024 999 2 .145 985 1 956 597 3 A26 906 1 1 323 979 4 725 853 330 012 2 831 389 068 3 999.180 2 021 112 1 3 .999 986 026 999 357 2 2 161 333 978 1 4 442 904.580 .113954 1 752 070 3 583 836 1 2 461 895 027 999 962 97 .190 4 .024 1 3 2 854 570 ,013 998 340 342 999 3 1 121 .985 999 345 075 2 2 .117 031 999 2 462 896 .600 4 .130 981 1 365 973 1 1778 199 ELO 090 999 999 983 980 819 .070 075 2 1 2 1 2 .080 085 .090 .822 .095 .027 999 1 342 977.190 3 031 999 2 365 973 1 .035 998 .200 3 388 969 2 .040 998 1 .410 965 210 3 .044 998 2 .432 960 1 .049 997 220 3 .454 955 2 054 997 1 .475 950 .230 3 .059 .997 2 ,496 945 1 .065 996 2403 516 939 2 .017 995 1 537 933 250 076 .995 2 59 927 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 .752 838 1 024 .998 3104 117 .980 3 .778 .819 2 .028 .998 1 .194 .976 380 4 801 .801 3 .032 .998 2 211 .973 1 .783 380 4 .036 .997 3 .229 .969 2 .842 .765 1 .041 .997.400 4 .247 .965 3 860 .747 2 .046 .996 1 .265 960.420 4 .876 730 3 ,052 .995 2 284 .955 1 890 712 440 4 962 583 .013 .999 121.985 462_896.600 .967.569 .017 998 .141.981 501 .880.650 975 542 .021 .998 163.976 540 .863.700 .981 .516 ,026 997 186 972 579,845 .750 986 493 .031 997 211 966 800 .616 826 989 471 037 996 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 4 3 2 A81 895 .854 B70 999 345 .130 981 A97 863 .875 652 .999 353 .179 .972 .588 850 .918 608 .999 308 .240 960 .878 815 .950 568 999286 316 944 .763 777 .972 532 410 924 .841 739 .987 500 .100 .105 .110 .115 .120 X M D F X M D F X MD FX MDF N-N- .142 Na .850 4 .522 900 064 1 .547 940.1352 .415.952 220 3 .907 702 068 2 .126 995 1 907.699 2 .995 470 1 .562 838 .140 4 .028 999 .900 4 .656 .871 068 3 .020 .999 3 .132.991 3 .957 .666 2 .133 994 2 .437.947 2.998 .444 1 .577 931 1 919.680230 .950 4 815 .838 070 3 .022 999 .145 4 032 .999 3 .989 631 2 .140 994 3 .144 .990 Population 10 1 .591 926 2 .480.941 2016 1 .144 997 075 3 026 999 1 .929.662 .0191 .170 996 2 158 992.150 4 .036 998 240 ,021 1 .188 995 1 627 913 3 .156 989 023 1 .206 994 .080 3 .031 999 2 .483.935 .025 1 224 993 2 .177.990 1 .939 644 026 1 .232 992 1 .660 899.1554 040 998 .028 1 .250 991 0853 037 999 3 .169.987 250 .030 1 268 990 2 .196 988 2 505 928 032 2 033 999 1 .692 .883 1 947 627 1 285 988.0903 ,043 998.160 4 .044 998 .034 2 037 .999 2 .216 986 3 .182.986 1 301 986 1 722 867 2 528 921 0362 .999 095 3 049 998 1 954.610 260 1 320 984 2 237 .984.165 4 .049997 038 2 046 999 1 750 850 3 .195 984 1 337 982 .100 3 .056 998 2 550 914 040 2 050 999 2 258 981 1 961 594 1 354 980 1 .776 832 .170 4 054 997 042 2 .055 999 .105 3 054 997 3 209.982 270 1 371 978 2 279 978 2 571 906 044 2 .060 998 1 800 814 1 966 579 1 388 975 110 3 072 997.1805 013999 046 2 055998 2 301 974 4 0B6 996 5 .030 998 4 .124 990 3 .386 954 2 .781 815 1 .993 453 5 .037 998 4 .988 3 400.947 2 .791 794 1 .995 434 5 044 997 4 .162 988 3 434 938 2 .819.774 1 996 416 6 2010 999 5 .052 997 4 .183 983 3 469 929 2 844 753 1 997 400 6 013999 5 060996 4 205 990 3 503 919 2 866 732 1 998 384 6 015999 5 070995 4 228 976 3 537 908 2 886 712 041 .044 .046 .048 .050 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2. 1 2 052 .055 999 .105 3 371 .978 2 060 998 1 388 975 110 3 .065 998 2 404 973 1 .071 1998 .115 3 .421 970 2 .076 998 1 .437.967.120 4 082997 3 ,454 963 2 .088 997 1 .470 960.125 4 094 997 3 486 956 2 100 996 501 953 130 4 .106 996 3 .517 949 2 .113 996 1 532 .945 -135 4 .119 995 3 4 997 3 279978 2 .800 _814 1 .072.997.1805 301 .974 4 .822.795 3 .081 .996 2 324 971 1 .843 776.190 5 2016 999 .090 995 3 346 967 2 861 756 1 .019 999 200 5 .100 994 4 369 962 3 .878 737 2 022 999 1 110 210 1392 958 4 896 718 3 .025 999 2 1.121 993 1 209.982 270 571 .906 .966 579 013 .999 .066 .998 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