chapters 1.2.4, 4s, 5, 5s, 9. & 18 Sved Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentially distributed and has a mean of 11 minutes per machine. The machines operate for an average of 77 minutes between adjustments. While running, each machine can turn out 60 pieces 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.) Probability b. Find the average number of machines waiting for adjustment (Round your answer to 2 decimal places.) Average number of machines waiting machines c. Find the average number of machines being serviced. (Round your answer to 2 decimal places.) Avage number of machines machines d. The expected hourly output of each machine, taking adjustments into account (Round your answer to 2 decimal places.) Edited only pieces e. Machine downtime represents a cost of $75 per hour operator cost (including salary and fringe benefits) is $10 per hour. What is the optimum number of operators? of operator O2 operators 3 operators 4 operators per gent Us AfD FX MDF XMD 125 Popolations 012 019 00 0036 040 FND TABLE 18.7 02994 20 575920 2 0933 2 305 1 554 914 270 3 164 4 096 353 04595 32 1 25 $12307 1 915570 102592 2503 07190 30 900 2 32208430 011909 1 100 991.250 4 11975 547852 99 415 012999 115 990 1 664 885 300 013990 122 989 68087 015 909 310 130 988 695359 054 2 1 060 990 1 1 095998130 2 1 125097 1 1 149 00135 2 1 160595 1 1 179 994140 2 1 1990 1 1 200902145 3 1 218 091 2 046 1 228 990 1 050 1 247 989 150 3 052 1 257958 2 1 286 987 1 056 2 018 999155 3 1 276 985 2 0582 019 999 1 1 285984.160 3 060 2 020 999 2 1 295 983 1 082 2 022 999 165 3 1 304 982 2. 054 2 023999 1 1 314 981170 3 066 2 .024.999 2 1 323 979 1 0682 026 999 180 3 1 333 978 2 070 2 027 999 1 1 342 977 190 3 075 2 .031 2 1 365 973 1 0802 035 998.200 3 1 388969 2 085 2 040 998 1 1 410 965 210 3 090 2 044 998 2 1 432 960 1 095 2 049 997.220 3 1 454 955 2 100 2 054 997 1 1 475 950 230 3 059.997 2 1 .496 945 1 110 2 065 996 240 3 1 516 939 2 2 .017 995 1 1 537 933.250 .120 2 076 995 2 1 556 927 .016 999 137 987 320 710861 2017 999 145 985 725853330 021 999 161983 .752 836 024 998340 117 980 .778 819 028998 194976360 801 801 .032 998 211 973 B22 783 380 + 994 953 007 900 0799 1 2 362 22 500 4 934544 3 4 30990 2 3 0860 1 97309 2 382 928 320 073901 + 0422 3 009990 2 779 728 3 094989 1 2 402919 5404 1 950513 330917 4 01092 2 306708 3 103 988 1 999 370 2 422 912 560 4 1 956 597 3 26 906 4 012999 2 831 889 3 112 986 1 2 442 9045804 113984 1 962 583 3 461295 4 2 013999 254570 3 121985 1 990365 2 4 130 S81 -1 967589 3 2 4 017 998 875 852 1 3 141 981 999 333 4 2 .179 972 3 975 542 588 550 1 2 918 508 4 021 998 1 3 163.976 4 700 2 240 960 540 863 3 678 315 1 981 516 2 S50 568 4 626 997 1 999286 3 4 316 94 2 3 783772 1 986 493 2 972 512 4 4 410324 3 3 341 739 2 2 987 500 999 462 196 500 501 380 650 1052 186 972 579 345 750 035 997 229969 842765 041 997 400 247 965 860 747 046 996 265 960 420 876730 052 995 284 955 890712 440 .115 031 997 211 968 300 516 26 99 47 037996 3 - 4 1 X MDF XANDFX DF XM DF 032 850 4 5222 300064 5450135 1 2 5 215 220 000 990 3 SOT 702066 1 2 907 890 4 124 900 3 2 995470 1 56290 140 366054 100 65671.000 2 2 020 900 3 132991 761 815 3 957 666 2 13394 2 947 1 993453 2 398444 1 577931 + 919500230 5 637 950 4 815 BOTO 3 022990 145 032999 4 142 98 3 300 831 2 140 994 3 144 990 3 400 947 Population 10 1 S01 25 2 450 941 2 791794 016 1 144997075 3 008 909 1 929 562 1 995434 019 1 170998 2 150992150 4 036998240 5 044997 021 1 188995 1 527 913 3 -1569 162 988 023 206 994 080 3 031 999 2 43935 3 434 938 025 1 224 993 2 177 990 1 $3951 2 819 774 025 1 282992 1 660899 155 4 000 998 1 996 416 028 1 250 991 085 3 037999 3 169987250 010990 030 1 268 990 2 196 SSB 2 SOS 928 5 052997 2 033999 1 382 383 1 917 27 4 183 980 1 285 958 090 3 043 998160 4 044998 3 469929 034 2 037999 216966 3 182 986 2 844 753 1 301 986 1 722357 528 921 1 997 400 036 2 041 999.095 3 049 998 1 954810260 6 013999 1 320 984 2 237 964 165 & 049997 5 060 986 030 2 046 999 1 750 850 3 195984 4 205 980 1 337982 100 3 056 998 2 550914 3 503 919 040 2 050 999 2 258961 1 951 594 2 366 732 1 354980 1 776 832 170 4 054 997 1 998 384 .042 2 055 999105 3 .064 997 3 209982270 6 015999 1 371978 2 279978 2 571 SOB 5 070 996 044 2 060 998 1 800314 1 966 579 4 228 976 1 388 975 110 3 072997180 5 013999 3 537 908 046 2 065 998 2 301 974 4 066998 2 886 712 1 404 973 1 822 795 3 238 978 1 999 370 048 2 071 998.115 3 081 996 2. 514890 280 6 018 999 1 421 970 2 324 971 1 975 890 5 2 076 998 081 994 1 843 776.190 5 016 999 4 252972 1 437 967120 4 2016 999 4 078 986 052 2 3 082 997 571 896 3 090 995 3 289973 454 963 2 1 903 592 2 346 967 2 554 873 054 2 088 997 1 999 357 1 861 756 1 982 522 290 1 470 960.125 6 022999 4 019 999 200 5 020999 056 2 094 997 5 093999 3 100 994 4 092 994 1 486 956 4 2 369 962 278 968 3 058 2 100 996 300 968 3 1 878 737 603 884 2 1 501953 130 692854 4 022 999 2 918 672 1 060 987 497 2 106 996 3 110 994 210 1 999 345 5 1 517 949 025999 300 6 2 026 998 4 138 992 062 2 -113 996 1 893 718 5 106 991 3 333961 1 532 945.135 4 025999 4 304 963 064 2 2 119 995 728835 3 .121 993 3 635 872 1 OSO -392 958 990474 continued Eighteen Management of Waiting Lines X MD F X M D F X MD FX MO 300 310 2 1 6 5 4 3 2 6 420 WOON 320 .330 4 3 2 6 5 4 3 2 7 6 5 4 932.653 400 .999 333 .031 .998 .120 990 .331 957 .666 858 943.635 .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 .014 999 .064 995 480 .205.978 474 .923 .798 787 .978 553 ..019 999 .083.993 .247 971 .500 -533 906 .840 758 .986 525 .026 998 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 8 7 6 5 4 3 2 8 7 6 F . 105.991 (CC 500 3 292 963 972 598 650 7 353 954 2 999 400 .591 887 520 6 .651 878 8 026998 .875 728 5 882759 7 .115 989 991 499 4 980 614 316 958 .034 993 3 999461 5 606 884 700 .130 987 9 .040 997 4 864 752 341 954 8 200 979 3 980 575 7 .646 866 .484 929 2 999 385 6 1772 836 .905 700 540 8 .034 997 5 940 711 .994 476 7 141 986 4 992571 .045 997 6 363 949.750 9 .075 994 160 984 5 .658 867 8 307 965 .392.943 4 .893 729 7 .626 897 .698 845 3 .986 555 6 870 792 .928.672 560 8 .044 996 5 .975 666 .996 454 7 .171 982 4 998 533 .011 999 6 .413 939.800 9 .134 988 .058 995 5 .707 848 8 446944 .193.979 4 .917 706 7 .763 859 445 930 3 1991 535 6 939.747 .747 822 580 8 .057 995 .991 625 .947.646 7 4 204 977 999 500 6 .998 435 9 465 927 850 232 979 5 .753 829 8 .611 916 4 .937 .684 7 .879 818 3 .994 517 6 .978 705 5 .010999 9 998 588 8 .072 994 .900 9 387 963 .242972 8 7 .785881 7 518 915 6 957 777 6 .995.667 5 -795809 9 .630 938 4 934 841 7 994 737 340 NO 360 2 7 6 5 4 3 380 2 7 6 .015 999 .074 994 -230 973 499 916 .600 .791 .799 .961 621 998 417 .020 999 .093.992 271 966 .553 901.650 .830 775 5 CO DO 4 3 2 8 7 6 5 4 c) O CO .953 663 950 996 500 .021 999 .123 988 2 400 7