{VERSION 2 3 "HP RISC UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT 260 21 "Pig problem Revisited" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;with(linalg);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 258 7 "Problem" }{TEXT -1 448 ": A pig f armer has resources of corn, tankage, and hay to make up a pig diet wh ich satisfies certain minimum daily requirements as to the basic nutri ents of carbohydrates, proteins, and vitamins. The table showing the \+ minimum amounts of each nutrient needed and the amount of each nutrien t in a kilogram of resource and the cost of the resource is given bel ow. Desired is a diet which satisfies the minimum daily requirement a t minimum cost. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 "tab \+ := matrix(5,5,[\n`Nutrients`,`corn(Kg)`,`tankage(Kg)`,`hay(Kg)`,`mdr`, \n`carbo`,90,20,40,200,\n`protein`,30,80,60,180,\n`vitamins`,10,20,60, 150,\n`cost(.01$)`,35,30,25,` `]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tabG-%'MATRIXG6#7'7'%*Nutrie ntsG%)corn(Kg)G%,tankage(Kg)G%(hay(Kg)G%$mdrG7'%&carboG\"#!*\"#?\"#S\" $+#7'%(proteinG\"#I\"#!)\"#g\"$!=7'%)vitaminsG\"#5F2F9\"$]\"7'%+cost(. 01$)G\"#NF7\"#D%#~~G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Setup: \+ Let c, t, and h denote the number of kg of corn, tankage, and hay per pig" }}{PARA 0 "" 0 "" {TEXT -1 80 "in the diet. Then the constraint s are linear inequalities in these quanitities." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 108 "cnsts := \{90*c + 20*t + 40*h >=200,\n \+ 30*c + 80*t + 60*h >=180,\n 10*c + 20*t + 60*h >=150\};" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&cnstsG<%1\"$+#,(%\"cG\"#!*%\"tG\"# ?%\"hG\"#S1\"$!=,(F)\"#IF+\"#!)F-\"#g1\"$]\",(F)\"#5F+F,F-F4" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "The cost is a linear function of t hese quantitities." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "cost \+ := 35*c + 30*t + 25*h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%costG,(% \"cG\"#N%\"tG\"#I%\"hG\"#D" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 " We can use the simplex package to solve this problem." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex);" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for basis" }}{PARA 7 "" 1 "" {TEXT -1 38 "Warning, new definition for convexhull" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for cterm" }}{PARA 7 "" 1 "" {TEXT -1 35 "Warning, new definition for display" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for dual" }}{PARA 7 "" 1 "" {TEXT -1 36 "W arning, new definition for feasible" }}{PARA 7 "" 1 "" {TEXT -1 36 "Wa rning, new definition for maximize" }}{PARA 7 "" 1 "" {TEXT -1 36 "War ning, new definition for pivoteqn" }}{PARA 7 "" 1 "" {TEXT -1 36 "Warn ing, new definition for pivotvar" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warni ng, new definition for ratio" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, \+ new definition for setup" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#71%&basisG %+convexhullG%&ctermG%,define_zeroG%(displayG%%dualG%)feasibleG%)maxim izeG%)minimizeG%&pivotG%)pivoteqnG%)pivotvarG%&ratioG%&setupG%,standar dizeG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "sol := minimize(co st,cnsts,NONNEGATIVE);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<%/% \"tG\"\"!/%\"cG#\"\")\"\"(/%\"hG#\"# " 0 "" {MPLTEXT 1 0 33 "subs(sol,[cost,cnsts]); evalf(\");" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7$#\"$0(\"\"(<%1\"$+#F)1\"$!=F+1\"$]\"#\"%+6F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+dG925!\"(<%1$\"$+#\"\"!F)1$\"$!= F+F-1$\"$]\"F+$\"+r&G9d\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 212 "S o, each pig should get no tankage, 17/7 kg of hay, and 8/7 kg of co rn each day at at cost of about 1100/7 dollars. The pig gets his mi nimum carbo and protein, and about 7 units over his minimum vitamins ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 " eqns := [a1 =lhs(cn sts[1])-rhs(cnsts[1])+s1,\na2 =lhs(cnsts[2])-rhs(cnsts[2])+s2,\na3 = lhs(cnsts[3])-rhs(cnsts[3])+s3]; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#> %%eqnsG7%/%#a1G,,\"$+#\"\"\"%\"cG!#!*%\"tG!#?%\"hG!#S%#s1GF*/%#a2G,,\" $!=F*F+!#IF-!#!)F/!#g%#s2GF*/%#a3G,,\"$]\"F*F+!#5F-F.F/F8%#s3GF*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "phase1cost := subs(eqns,a1 \+ +a2 +a3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+phase1costG,0\"$I&\"\" \"%\"cG!$I\"%\"tG!$?\"%\"hG!$g\"%#s1GF'%#s2GF'%#s3GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "tabular(eqns,phase1cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7'7,%#a1G%#a2G%#a3G%\"cG%\"hG%#s 1G%#s2G%#s3G%\"tG%\"ZG7,\"\"!F3F3!$I\"!$g\"\"\"\"F6F6!$?\"\"$I&7,F6F3F 3\"#!*\"#S!\"\"F3F3\"#?\"$+#7,F3F6F3\"#I\"#gF3F " 0 "" {MPLTEXT 1 0 14 "pivot var := h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivotvarG%\"hG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "pivoteqn := eqns[3];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%#a3G,,\"$]\"\"\"\"%\"cG! #5%\"tG!#?%\"hG!#g%#s3GF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "pivoteqn := op(solve(pivoteqn ,\{pivotvar\})) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%\"hG,,%#a3G#!\"\"\"#g#\"\"&\"\"#\"\" \"%\"cG#F*\"\"'%\"tG#F*\"\"$%#s3G#F/F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "eqns2 := [subs(pivoteqn,eqns[1]),subs(pivoteqn,eqns[2 ]),pivoteqn];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&eqns2G7%/%#a1G,.\" $+\"\"\"\"%\"cG#!$]#\"\"$%\"tG#!#?F.%#a3G#\"\"#F.%#s3G#!\"#F.%#s1GF*/% #a2G,.\"#IF*F+F1F/!#gF2F*F5!\"\"%#s2GF*/%\"hG,,F2#F>\"#g#\"\"&F4F*F+#F >\"\"'F/#F>F.F5#F*FD" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "pha se1cost := subs(pivoteqn,phase1cost) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+phase1costG,0\"$I\"\"\"\"%\"cG#!$5$\"\"$%\"tG#!$+#F+%#a3G#\" \")F+%#s3G#!\"&F+%#s1GF'%#s2GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "tabular(eqns2,phase1cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%'MATRIXG6#7'7,%#a1G%#a2G%#a3G%\"cG%\"hG%#s1G%#s2G%#s3G%\"tG%\"ZG7,\" \"!F3#\"\")\"\"$#!$5$F6F3\"\"\"F9#!\"&F6#!$+#F6\"$I\"7,F9F3#!\"#F6#\"$ ]#F6F3!\"\"F3#\"\"#F6#\"#?F6\"$+\"7,F3F9FDFHF3F3FDF9\"#g\"#I7,F3F3#F9F K#F9\"\"'F9F3F3#FDFK#F9F6#\"\"&FF" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "pivotvar := c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%) pivotvarG%\"cG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ratios := 100/(250/3),30/20, (5/2)/(1/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% &ratioG6%#\"\"'\"\"&#\"\"$\"\"#\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pivoteqn := eqns2[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%#a1G,.\"$+\"\"\"\"%\"cG#!$]#\"\"$%\"tG#!#?F-%#a3G# \"\"#F-%#s3G#!\"#F-%#s1GF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "pivoteqn := op( solve(pivoteqn ,\{pivotvar\}) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%\"cG,.%#a1G#!\"$\"$]##\"\"'\"\"&\"\"\" %#s1G#\"\"$F+%\"tG#!\"#\"#D%#a3G#F/\"$D\"%#s3G#!\"\"F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "eqns3 := [pivoteqn,subs(pivoteqn,eq ns2[2]), subs(pivoteqn,eqns2[3]) ]; \n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&eqns3G7%/%\"cG,.%#a1G#!\"$\"$]##\"\"'\"\"&\"\"\"%#s1G#\"\"$F, %\"tG#!\"#\"#D%#a3G#F0\"$D\"%#s3G#!\"\"F:/%#a2G,0F.F0F)#F.F7F1#!\"'F7F 4#!$#HF/F8#\"#@F7F;#!#@F7%#s2GF0/%\"hG,.F8#!\"*\"$+&#\"#B\"#5F0F)#F0FP F1#F=FPF4#!\")F7F;#\"\"*FP" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "phase1cost := subs(pivoteqn,phase1cost) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+phase1costG,0\"\"'\"\"\"%#a1G#\"#J\"#D%#s1G#!\"'F+% \"tG#!$#H\"\"&%#a3G#\"#YF+%#s3G#!#@F+%#s2GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "tabular(eqns3,phase1cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7'7,%#a1G%#a2G%#a3G%\"cG%\"hG%#s1G%#s2G%#s3 G%\"tG%\"ZG7,#\"#J\"#D\"\"!#\"#YF5F6F6#!\"'F5\"\"\"#!#@F5#!$#H\"\"&\" \"'7,#\"\"$\"$]#F6#!\"\"\"$D\"F;F6#!\"$FEF6#F;FH#\"\"#F5#FAF@7,F9F;F " 0 "" {MPLTEXT 1 0 14 "pivotvar := t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivotvarG%\"tG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ratios := 6/5/(2/25),6/(292/5),23/1 0/(8/25);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ratioG6%\"#:#F&\"$Y\"# \"$:\"\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " pivoteqn := \+ eqns3[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%#a2G,0\"\"' \"\"\"%#a1G#F(\"#D%#s1G#!\"'F,%\"tG#!$#H\"\"&%#a3G#\"#@F,%#s3G#!#@F,%# s2GF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "pivoteqn := op( so lve(pivoteqn ,\{pivotvar\}) );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)p ivoteqnG/%\"tG,0%#a2G#!\"&\"$#H#\"#:\"$Y\"\"\"\"%#a1G#\"\"$\"$I(%#s1G# !\"$F3%#a3G#\"#@\"%g9%#s3G#!#@F:%#s2G#\"\"&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "eqns4 := [subs(pivoteqn,eqns3[1]),pivoteqn, subs (pivoteqn,eqns3[3])]; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&eqns4G7%/ %\"cG,0%#a1G#!\"*\"$I(#\"#()\"#t\"\"\"%#s1G#\"\"*F,%#a2G#F0F,%#a3G#F0 \"$Y\"%#s3G#!\"\"F8%#s2G#F;F,/%\"tG,0F4#!\"&\"$#H#\"#:F8F0F)#\"\"$F,F1 #!\"$F,F6#\"#@\"%g9F9#!#@FLF<#\"\"&FC/%\"hG,0F6#!#LFL#\"$J$F8F0F)#F0FL F1#F;FLF4#\"\"#\"$l$F9#\"#LFLF<#!\"#Ffn" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "phase1cost := subs(pivoteqn,phase1cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+phase1costG,(%#a1G\"\"\"%#a2GF'%#a3GF'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "tabular(eqns4,phase1cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7'7,%#a1G%#a2G%#a3G%\"cG %\"hG%#s1G%#s2G%#s3G%\"tG%\"ZG7,\"\"\"F3F3\"\"!F4F4F4F4F4F47,#\"\"*\"$ I(#!\"\"F8#F:\"$Y\"F3F4#!\"*F8#F3F8#F3F " 0 "" {MPLTEXT 1 0 37 "eqns \+ := subs(\{a1=0,a2=0,a3=0\},eqns4);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%%eqnsG7%/%\"cG,*#\"#()\"#t\"\"\"%#s1G#\"\"*\"$I(%#s3G#!\"\"\"$Y\"%#s 2G#F3F0/%\"tG,*#\"#:F4F,F-#!\"$F0F1#!#@\"%g9F5#\"\"&\"$#H/%\"hG,*#\"$J $F4F,F-#F3F@F1#\"#LF@F5#!\"#\"$l$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "cost := subs(eqns,co st);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%costG,*#\"&:[\"\"$Y\"\"\"\" %#s1G#\"#&)\"$#H%#s3G#!#JF-%#s2G#\"#C\"#t" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "tabular(eqns,cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7'7)%\"cG%\"hG%#s1G%#s2G%#s3G%\"tG%\"ZG7)\"\"!F0#\"# &)\"$#H#\"#C\"#t#!#JF3F0#\"&:[\"\"$Y\"7)\"\"\"F0#!\"*\"$I(#F=F@#F=F;F0 #\"#()F67)F0F0#\"\"$F@#!\"&F3#\"#@\"%g9F=#\"#:F;7)F0F=#F=FL#\"\"#\"$l$ #!#LFLF0#\"$J$F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "pivotva r := s3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivotvarG%#s3G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "ratios := 87/73/(1./146),21/ 1460/(15/146.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ratioG6$$\"++++S " 0 "" {MPLTEXT 1 0 20 "pivote qn := eqns[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%\"tG,* #\"#:\"$Y\"\"\"\"%#s1G#!\"$\"$I(%#s3G#!#@\"%g9%#s2G#\"\"&\"$#H" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "pivoteqn := op(solve(pivoteq n,\{pivotvar\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)pivoteqnG/%#s3 G,*%\"tG#!%g9\"#@#\"#]\"\"(\"\"\"%#s1G#!\"#F.%#s2G#\"#DF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "eqns2 := [subs(pivoteqn,eqns[1]),pi voteqn, subs(pivoteqn,eqns[3])];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% &eqns2G7%/%\"cG,*#\"\")\"\"(\"\"\"%#s1G#F,\"#q%\"tG#\"#5\"#@%#s2G#!\" \"\"$0\"/%#s3G,*F0#!%g9F3#\"#]F+F,F-#!\"#F+F4#\"#DF3/%\"hG,*#\"# " 0 "" {MPLTEXT 1 0 28 "cost := subs(pivoteqn,cost);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%%costG,*#\"$0(\"\"(\"\"\"%#s1G#\"\"*\"#G%\"tG#\"$b\"\"#@%#s2G#\"#<\" #%)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "tabular(eqns2,cost); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7'7)%\"cG%\"hG%#s1G%#s 2G%#s3G%\"tG%\"ZG7)\"\"!F0#\"\"*\"#G#\"#<\"#%)F0#\"$b\"\"#@#\"$0(\"\"( 7)\"\"\"F0#!\"\"\"#q#F>\"$0\"F0#!#5F9#\"\")F<7)F0F0#\"\"#F<#!#DF9F>#\" %g9F9#\"#]F<7)F0F>#F>\"$S\"#!\"$FSF0#\"#6F<#F5F<" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 109 "End of phase 2. The minimum cost diet is 8/7 kg \+ of corn, 17/7 kg hay, 0 tankage for a cost of 705/7 dollars." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#-%'MATRIXG6#7'7)%\"cG%\"hG%#s1G%#s2G%#s3G%\"tG%\"ZG7) \"\"!F0$\"+9dG9K!#5$\"+C&4Q-#F3F0$\"+\"Q_4Q(!\"*$\"+dG925!\"(7)$\"\"\" F0F0$!+H9dG9!#6$\"+C&4Q_*!#7F0$!+iZ!>w%F3$\"+Vr&G9\"F87)F0F0$\"+dG9dGF 3$!+!>w/>\"F8F=$\"+_4Q_p!\")$\"+Vr&G9(F87)F0F=$FRFD$!+Vr&G9#FAF0$\"+r& G9d\"F8$\"+H9dGCF8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "Questions" {TEXT -1 1 " " }{TEXT 256 9 "Questions" }{TEXT -1 3 ": " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "1. How low would the price of tank age have to get before it would be used in the pig diet?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 116 "2. How l ow would the amount of vitamins in hay have to get before it becomes \+ economical to use tankage in the diet?" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 97 "3. Suppose there is only 2 kg of hay \+ per pig available. What is the minimum cost pig diet then?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 204 "4. Suppose the re is an additional resource of sardine meal costing 33 cents per kg and containing 60, 40, and 15 units of carbo, protein, and vitamins \+ respectively. What is the minimum cost diet then?" }}}{EXCHG {PARA 0 "" 0 "bottom" {HYPERLNK 17 "Table of Contents" 1 "ma416s97.mws" "top" }}}}}{MARK "0 1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }