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Question 12.SP.7: What safety stock should Ron Satterfield Corporation maintai...

What safety stock should Ron Satterfield Corporation maintain if mean sales are 80 during the reorder period, the standard deviation is 7, and Ron can tolerate stockouts 10% of the time?

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From Appendix I, Z at an area of .9 (or 1 – .10) = 1.28, and Equation (12-14):
Safety stock = Z\sigma_{dLT}
= 1.28(7) = 8.96 units, or 9 units

TABLE I.1
Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
.0 .50000 .50399 .50798 .51197 .51595 .51994 .52392 .52790 .53188 .53586
.1 .53983 .54380 .54776 .55172 .55567 .55962 .56356 .56749 .57142 .57535
.2 .57926 .58317 .58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409
.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173
.4 .65542 .65910 .66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793
.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 .71566 .71904 .72240
.6 .72575 .72907 .73237 .73565 .73891 .74215 .74537 .74857 .75175 .75490
.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524
.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327
.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891
1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214
1.1 .86433 .86650 .86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298
1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147
1.3 .90320 .90490 .90658 .90824 .90988 .91149 .91309 .91466 .91621 .91774
1.4 .91924 .92073 .92220 .92364 .92507 .92647 .92785 .92922 .93056 .93189
1.5 .93319 .93448 .93574 .93699 .93822 .93943 .94062 .94179 .94295 .94408
1.6 .94520 .94630 .94738 .94845 .94950 .95053 .95154 .95254 .95352 .95449
1.7 .95543 .95637 .95728 .95818 .95907 .95994 .96080 .96164 .96246 .96327
1.8 .96407 .96485 .96562 .96638 .96712 .96784 .96856 .96926 .96995 .97062
1.9 .97128 .97193 .97257 .97320 .97381 .97441 .97500 .97558 .97615 .97670
2.0 .97725 .97784 .97831 .97882 .97932 .97982 .98030 .98077 .98124 .98169
2.1 .98214 .98257 .98300 .98341 .98382 .98422 .98461 .98500 .98537 .98574
2.2 .98610 .98645 .98679 .98713 .98745 .98778 .98809 .98840 .98870 .98899
2.3 .98928 .98956 .98983 .99010 .99036 .99061 .99086 .99111 .99134 .99158
2.4 .99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361
2.5 .99379 .99396 .99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520
2.6 .99534 .99547 .99560 .99573 .99585 .99598 .99609 .99621 .99632 .99643
2.7 .99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .99736
2.8 .99744 .99752 .99760 .99767 .99774 .99781 .99788 .99795 .99801 .99807
2.9 .99813 .99819 .99825 .99831 .99836 .99841 .99846 .99851 .99856 .99861
3.0 .99865 .99869 .99874 .99878 .99882 .99886 .99889 .99893 .99896 .99900
3.1 .99903 .99906 .99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929
3.2 .99931 .99934 .99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950
3.3 .99952 .99953 .99955 .99957 .99958 .99960 .99961 .99962 .99964 .99965
3.4 .99966 .99968 .99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976
3.5 .99977 .99978 .99978 .99979 .99980 .99981 .99981 .99982 .99983 .99983
3.6 .99984 .99985 .99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989
3.7 .99989 .99990 .99990 .99990 .99991 .99991 .99992 .99992 .99992 .99992
3.8 .99993 .99993 .99993 .99994 .99994 .99994 .99994 .99995 .99995 .99995
3.9 .99995 .99995 .99996 .99996 .99996 .99996 .99996 .99996 .99997 .99997
TABLE I.2
Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.0 .00000 .00399 .00798 .01197 .01595 .01994 .02392 .02790 .03188 .03586
0.1 .03983 .04380 .04776 .05172 .05567 .05962 .06356 .06749 .07142 .07535
0.2 .07926 .08317 .08706 .09095 .09483 .09871 .10257 .10642 .11026 .11409
0.3 .11791 .12172 .12552 .12930 .13307 .13683 .14058 .14431 .14803 .15173
0.4 .15542 .15910 .16276 .16640 .17003 .17364 .17724 .18082 .18439 .18793
0.5 .19146 .19497 .19847 .20194 .20540 .20884 .21226 .21566 .21904 22240
0.6 .22575 .22907 .23237 .23565 .23891 .24215 .24537 .24857 .25175 .25490
0.7 .25804 .26115 .26424 .26730 .27035 .27337 .27637 .27935 .28230 .28524
0.8 .28814 .29103 .29389 .29673 .29955 .30234 .30511 .30785 .31057 .31327
0.9 .31594 .31859 .32121 .32381 .32639 .32894 .33147 .33398 .33646 .33891
1.0 .34134 .34375 .34614 .34850 .35083 .35314 .35543 .35769 .35993 .36214
1.1 .36433 .36650 .36864 .37076 .37286 .37493 .37698 .37900 .38100 .38298
1.2 .38493 .38686 .38877 .39065 .39251 .39435 .39617 .39796 .39973 .40147
1.3 .40320 .40490 .40658 .40824 .40988 .41149 .41309 .41466 .41621 .41174
1.4 .41924 .42073 .42220 .42364 .42507 .42647 .42786 .42922 .43056 .43189
1.5 .43319 .43448 .43574 .43699 .43822 .43943 .44062 .44179 .44295 .44408
1.6 .44520 .44630 .44738 .44845 .44950 .45053 .45154 .45254 .45352 .45449
1.7 .45543 .45637 .45728 .45818 .45907 .45994 .46080 .46164 .46246 .46327
1.8 .46407 .46485 .46562 .46638 .46712 .46784 .46856 .46926 .46995 .47062
1.9 .47128 .47193 .47257 .47320 .47381 .47441 .47500 .47558 .47615 .47670
2.0 .47725 .47778 .47831 .47882 .47932 .47982 .48030 .48077 .48124 .48169
2.1 .48214 .48257 .48300 .48341 .48382 .48422 .48461 .48500 .48537 .48574
2.2 .48610 .48645 .48679 .48713 .48745 .48778 .48809 .48840 .48870 .48899
2.3 .48928 .48956 .48983 .49010 .49036 .49061 .49086 .49111 .49134 .49158
2.4 .49180 .49202 .49224 .49245 .49266 .49286 .49305 .49324 .49343 .49361
2.5 .49379 .49396 .49413 .49430 .49446 .49461 .49477 .49492 .49506 .49520
2.6 .49534 .49547 .49560 .49573 .49585 .49598 .49609 .49621 .49632 .49643
2.7 .49653 .49664 .49674 .49683 .49693 .49702 .49711 .49720 .49728 .49736
2.8 .49744 .49752 .49760 .49767 .49774 .49781 .49788 .49795 .49801 .49807
2.9 .49813 .49819 .49825 .49831 .49836 .49841 .49846 .49851 .49856 .49861
3.0 .49865 .49869 .49874 .49878 .49882 .49886 .49889 .49893 .49897 .49900
3.1 .49903 .49906 .49910 .49913 .49916 .49918 .49921 .49924 .49926 .49929
capture-20211212-213345

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