{\rtf1\ansi \deff0{\colortbl;\red0\green0\blue0;\red128\green0\blue0; \red0\green128\blue0;\red128\green128\blue0;\red0\green0\blue128;\red128 \green0\blue128;\red0\green128\blue128;\red128\green128\blue128;\red192 \green192\blue192;\red255\green0\blue0;\red0\green255\blue0;\red255 \green255\blue0;\red0\green0\blue255;\red255\green0\blue255;\red0 \green255\blue255;\red255\green255\blue255;}{\fonttbl{\f0\fcharset0 \fnil Arial;}}{\stylesheet{\f0\fs20 Normal;}{\s1\f0\fs28\b \sbasedon0 Überschrift 1;}{\s2\f0\fs24\b\i \sbasedon0 Überschrift 2;}{\s3\f0\fs24 \sbasedon0 Überschrift 3;}{\s4\f0\fs20 \li2160\fi2160 \sbasedon0 Einzug;}{\s5\f0\fs20 \li270\fi-285 \sbasedon0 Liste;}{\s6\f0\fs20 \fi420 \sbasedon0 Absatz;}{\s7\f1\fs36 \qc \sbasedon0 Untertitel;}{\s8\f1\fs48 \b \qc \sbasedon0 Titel;}}\plain\fs20 \pard\phmrg\pvmrg\posx256\posy1759 \absw8655\absh1200\plain\s0\f0\fs20 \pard\phmrg\pvmrg\posx256\posy1759 \absw8655\absh1200 Von einem Ort A ist für die Verlegung einer Gasleitung ein Graben zuerst längs einer geradlinig verlaufenden Straße und dann durch schwieriges Gelände zu einem abgelegenen Wellness-Hotel zu legen. Die verrechneten Grabungskosten im Gelände betragen Euro 75.-, die entlang der Straße Euro 30.- pro Meter. \par \pard\phmrg\pvmrg\posx2182\posy2448\absw6064\absh2550{\object{ \*\objclass \eqn}\rsltpict{\*\objdata }{\result {\pict\dn255\wmetafile8 \picw10160\pich4498\picwgoal5760\pichgoal2550 0100090000034504000008001c00000000000400000003010800050000000c02aa008001050000 000b0200000000050000002e0100000000030000001e00030000001e001400000026060f001e00 ffffffff040014000000576f72640e004d6963726f736f667420576f7264050000000c02270460 09050000000b02000000001c000000fb021000070000000000bc02000000000102022253797374 656d007740000000c60a0a03e6c0f477efc0f4770100000000003000040000002d010000050000 000201010000001c000000fb029cff0000000000009001000000000440001254696d6573204e65 7720526f6d616e00e6c0f477efc0f4770100000000003000040000002d01010005000000090200 0000020d000000320a0000000001000400000000006009270420302d001000000026060f001600 ffffffff000085000000dd020000a30500000003000008000000fa020500010000000000000004 0000002d01020007000000fc020000000000000000040000002d01030005000000060102000000 0c000000240304009600de029600ff029105ff029105de020500000006010100000008000000fa 0200000000000000000000040000002d01040007000000fc020000ffffff000000040000002d01 050004000000f00103000800000026060f000600ffffffff010007000000fc0200000000000000 00040000002d01030008000000fa0200000600000000000002040000002d010600070000001b04 e600bb059a006f05040000002d01050004000000f0010300040000002d01040004000000f00106 001000000026060f001600ffffffff00008a050000c800000093050000de02000008000000fa02 00000600000000000000040000002d01030007000000fc020100000000000000040000002d0106 0008000000250302008e05d9028e05cc00040000002d01040004000000f0010300040000002d01 05000800000026060f000600ffffffff01001000000026060f001600ffffffff00008d050000ea 0200000d070000f302000008000000fa0200000600000000000000040000002d01030004000000 2d01060008000000250302009105ee020807ee02040000002d01040004000000f0010300040000 002d0105000800000026060f000600ffffffff01001000000026060f001600ffffffff0000c005 0000b800000004070000c400000008000000fa0200000600000000000000040000002d01030004 0000002d0106000800000025030200c405bc00ff06bf00040000002d01040004000000f0010300 040000002d0105000800000026060f000600ffffffff01001000000026060f001600ffffffff00 0095060000c1000000e3060000f302000008000000fa0200000600000000000000040000002d01 0300040000002d0106000800000025030200ba060401bd06af02040000002d01020004000000f0 01030007000000fc020000000000000000040000002d0103000a00000024030300db060701ba06 c6009a0607010a000000240303009d06ad02be06ee02de06ad02040000002d010400040000002d 01050004000000f00103000800000026060f000600ffffffff0100040000002d01060004000000 2d010200070000001b040e02160977010807040000002d010500040000002d010400030000001e 00070000001604ef01da0895014407050000000201010000001c000000fb02adff000000000000 90010000000004400022417269616c00f47740000000d40a0a15e6c0f477efc0f4770100000000 003000040000002d01030013000000320a980144070500040044079501d908ef01373030206d00 2e002e002e00170047000d000000320a98012c080100040044079501d908ef0120002d00040000 002701ffff1000000026060f001600ffffffff000092000000ea0200009b0000001f0400000800 0000fa0200000600000000000000040000002d010700040000002d010600080000002503020096 00ee0296001a04040000002d01040004000000f0010700040000002d0105000800000026060f00 0600ffffffff01001000000026060f001600ffffffff00008d050000ea020000960500001f0400 0008000000fa0200000600000000000000040000002d010700040000002d010600080000002503 02009105ee0291051a04040000002d01040004000000f0010700040000002d0105000800000026 060f000600ffffffff01001000000026060f001600ffffffff000091000000aa03000095050000 f503000008000000fa0200000600000000000000040000002d010700040000002d010600080000 0025030200d400cf035105cf03040000002d01020004000000f001070007000000fc0200000000 00000000040000002d0107000a00000024030300d700af039600d003d700f0030a000000240303 004f05f0039005d0034f05af03040000002d010400040000002d01050004000000f00107000800 000026060f000600ffffffff0100040000002d010600040000002d010200070000001b04d0031b 0439030d02040000002d010500040000002d010400030000001e00070000001604b103df035703 490205000000020101000000040000002d0103000500000009020000000214000000320a5a0349 020600040049025703de03b10333303030206d2e002e002e002f00170047000d000000320a5a03 60030100040049025703de03b10320002c00040000002701ffff040000002d010600040000002d 010200070000001b04ef022d0158024b00040000002d010500040000002d010400030000001e00 070000001604d002f1007602870005000000020101000000040000002d01030005000000090200 0000020d000000320a790287000100040087007602f000d002410037000d000000320a7902be00 0100040087007602f000d00220002e00040000002701ffff040000002d01000004000000f00101 0004000000f0010300040000002701ffff040000002701ffff050000002e010000000003000000 0000}}}\par \pard\phmrg\pvmrg\posx256\posy5186\absw8594\absh1440\plain \s0\f0\fs20 \pard\phmrg\pvmrg\posx256\posy5186\absw8594\absh1440 a.) \tab Wie lang soll entlang der Straße gegraben werden, damit die verrechneten Kosten \tab minimal sind? Berechnen Sie zuerst allgemein, dann mit den entsprechenden Zahlen!\par \par \pard\phmrg\pvmrg\posx256 \posy5186\absw8594\absh1440\plain\s0\f0\fs20 \pard\phmrg\pvmrg\posx256 \posy5186\absw8594\absh1440 b.)\tab Um wieviel Prozent ist dieser Betrag kleiner gegenüber den Grabungskosten wenn man \tab von der Straße im rechten Winkel zum Hotel gräbt?\par \pard\phmrg\pvmrg\posx256 \posy7022\absw8691\absh960\plain\s0\f0\fs20 \pard\phmrg\pvmrg\posx256 \posy7022\absw8691\absh960 Die Erdbewegungsfirma kalkuliert entlang der Straße mit folgender Kostenfunktion: K(x) = 5x + 200. Betrachtet man die Anzahl der in Auftrag gegebenen Meter als Stückzahl, so hat sich nach langjähriger Beobachtung folgende Funktion für den Verkaufspreis pro Meter bewährt:\par \pard\phmrg\pvmrg\posx256\posy8001 \absw2103\absh555{\object{\*\objclass \eqn}\rsltpict{\*\objdata }{ \result {\pict\dn24\wmetafile8\picw1984\pich979\picwgoal1125\pichgoal555 0100090000030002000007001c00000000000400000003010800050000000c0225004b00050000 000b020000000008000000fa0200000100000000000002040000002d01000007000000fc020000 ffffff020000040000002d01010005000000090200000000050000000102ffffff020500000002 0101000000050000000902000000001c000000fb02f3ff00000000000090010000000004000000 54696d6573204e657720526f6d616e00e6c0f477efc0f4770100000000003000040000002d0102 00050000002e011800000005000000090200000000070000002105010076001600020005000000 090200000000050000000902000000000700000021050100780016000e00050000000902000000 001c000000fb020c00090000000000900100000000000202024d532053616e7320536572696600 040000000000ffffffff0100000000003000040000002d010300040000002d0102000700000021 0501002800160009000700000021050100290016001300050000000902000000001c000000fb02 f3ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e6c0f477ef c0f4770100000000003000040000002d0104000700000021050200383016002700050000000902 00000000040000002d01020005000000090200000000070000002105010078000d004400050000 0009020000000005000000090200000000040000002d0104000700000021050100320021004400 05000000090200000000040000002d010200050000000902000000001c000000fb02f3ff000000 0000009001000000020700000053796d626f6c007740000000dc090aa0e6c0f477efc0f4770100 000000003000040000002d01050008000000fa0200000100000000000002040000002d01060005 00000014021200430005000000130212004a00040000002d01000004000000f001060005000000 090200000000040000002d01020005000000090200000000040000002d010500050000002e0118 00000007000000210501002d0016003700050000002e0118000000050000000902000000000400 00002d01020005000000090200000000040000002d010500030000001e00070000001604240022 0001001c0005000000140214001b000500000013021400230005000000140211001b0005000000 130211002300040000002701ffff040000002d01000005000000090200000000040000002d0102 00050000002e010000000005000000090200000000040000002d01030008000000fa0200000000 000000000000040000002d01060004000000f001000007000000fc020000000000000000040000 002d01000004000000f001010005000000090200000000050000000102ffffff02050000000201 02000000030000000000}}}\par \pard\phmrg\pvmrg\posx256\posy8736\absw8482 \absh1920\plain\s0\f0\fs20 \pard\phmrg\pvmrg\posx256\posy8736\absw8482 \absh1920 c.)\tab Ermitteln Sie die Erlös- und die Gewinnfunktion! Bestimmen Sie die Gewinnschwellen!\par \par d.)\tab Zeichnen Sie die Graphen der Verkaufspreis-, der Kosten-, der Erlös- und der \tab Gewinnfunktion!\par \par e.)\tab Bei welchem Verkaufspreis würde die Firma einen max. Gewinn erzielen?\par \par f.)\tab Berechnen Sie die Fläche zwischen der Erlös- und der Kostenfunktion!\par \pard\phmrg \pvmrg\posx5521\posy10771\absw3597\absh2160{\object{\*\objclass \eqn} \rsltpict{\*\objdata }{\result {\pict\dn216\wmetafile8\picw5794\pich3810 \picwgoal3285\pichgoal2160 0100090000036d02000005002c00000000000400000003010800050000000c029000db00050000 000b0200000000050000002e0100000000030000001e00030000001e001400000026060f001e00 ffffffff040014000000576f72640e004d6963726f736f667420576f7264050000000c02840358 05050000000b02000000001c000000fb029cff0000000000009001000000000440002241726961 6c00f47740000000cf0a0a07e6c0f477efc0f4770100000000003000040000002d010000050000 00020101000000050000000902000000000500000002010100000007000000fc020000ffffff00 0000040000002d01010008000000fa0200000600000000000002040000002d010200070000001b 049f02bb044600fa0007000000fc020000ffffff000000040000002d01030004000000f0010100 08000000fa0200000000000000000000040000002d01010004000000f0010200030000001e0007 00000016047d027c04670039011c000000fb02adff000000000000900100000000044000224172 69616c00f47740000000d10a0a24e6c0f477efc0f4770100000000003000040000002d01020005 0000000201010000000500000014026a003901050000002e01010000002c000000320a6a003901 160004000000000058058403496e74657270726574696572656e205369652064696517002e0017 002e001c002e001c002e00180012002e001c002f002e001700380012002e0018002e0013002e00 050000002e01000000000500000014020000000005000000020101000000050000000201010000 00050000001402ca003901050000002e010100000020000000320aca0039010e00040000000000 5805840345726765626e6973736520756e6437001c002e002e002f002e0012002a002a002e0017 002f002e002e00050000002e010000000005000000140200000000050000000201010000000500 00000201010000000500000014022a013901050000002e010100000025000000320a2a01390111 0004000000000058058403646f6b756d656e74696572656e20536965002e002e002b002d004700 2e002e00170012002e001c002e002e001800380012002e00050000002e01000000000500000014 020000000005000000020101000000050000000201010000000500000014028a01390105000000 2e010100000028000000320a8a013901130004000000000058058403616c6c652052656368656e 766f7267e46e67656c2e00120013002e0017003c002e002a002f002e002f0029002e001c002f00 2e002e002f002e00050000002e0100000000050000001402000000000500000002010100000005 000000020101000000050000001402ea013901050000002e01010000002c000000320aea013901 16000400000000005805840373617562657220756e64206f7264656e746c696368212a002e002e 002e002e001c0017002f002e002e0018002e001c002e002e002e001800130012002a002e001900 050000002e01000000000500000014020000000005000000020101000000040000002701ffff1c 000000fb021000070000000000bc02000000000102022253797374656d007740000000c60a0a04 e6c0f477efc0f4770100000000003000040000002d01040004000000f001000004000000f00102 00040000002701ffff040000002701ffff050000002e0100000000030000000000}}} \par }