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Title: An Introduction to Spreadsheet Optimization Using Excel Solver Author: Joern Meissner Subject: An Introduction to Spreadsheet Optimization Using Excel Solver

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1 &! . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!! '. '! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!! (. (! . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!! , )! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!! , *! . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! &%. ,! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! &%. -! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! &'..! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!! &(. &%! . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!! &). &&! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! &*.. "" ! ! " " . " . ! .. & .. !# # .. # .. & " $ . " .. # & . # .. $ . " # .. $ .. # . % . " .. $ .. # . " . $ !!! .. $ " .. # .. $ .. $ . $ " " ! ! " " " ( " ! " " ' " ( " ! . ! " # !)))

2 " ! ! ! "+ " " ! " " ' . ' % " #! ! ! "!+ ! ! " ' %! . ! % " ' ! !" "! " " ! $ # ' ! ! " $ "+ . $ & # ! $ !" !* . /+ " ! ! " % ! " + . 0+ ' " % " ! " " $ # " + . 1+ ' " ! $ !+ . 2+ ' " ! % " !" "!+ . 3+ $ " ) + +) " ( + . !" " !! ! ! " % ! " !+ # ! " " ! " & . ! /0 %! + .. % #! # " & & " #!" " % " " & + . !" % ' #!" % ' ! " "% "' ! , !" . !" . - " # "! &" ! "+ " ! " !# ' "! " " #! .. ".. # ! $ #"- !! "# ! ! $ ! " 53 "- ! * 5 )"- "* 43 "- #* . ( " 153 ! #- !! "# ! ! $ ! " 4 )- "* 63 "- #* ( " . 163 ! #- ( " 833 "- ! * 93 )"- "* :33 "- # - . # & " " # # ! # $ # ! $ # ' ) ! #"- . "& ! # " $ "# * & # ! # " ! " # & & $ # # ! # # . $ # ! #" $" ! ( $ # ! ! ! ! $ - $! 6 " &" . # # " ! " # . !$ # # " " # "- # #! " . " & # " ! " # $! 6 ! $ ! % $ "* - -* ! $ " % # ! ( #- . " 7 7 # # $ #" "# ! "# ! # ! $ . # ! - ! # #! $# " ! ! $ # ! # # " 8 . 8- $ # ! # ! $ ! ! $ # ! $ # " % " 43, 45- . $ # #( ! #" % # ! " "# ! " 43, 45- .. ! !( " ! " #.))

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

10 ( " % ! # . ( . " & " $( . ! ! ! $( ) " * " . & ) * & ( . " ) * ! ( " . # (.))))


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