最优化理论与算法答案解析

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1、Æ/$4xP118ex1(1).:minz=−9x1−16x2s.t.x1+4x2+x3=802x1+3x2+x4=90xj≥0,j=1,2,3,4!"!>EXx3,x4,X5Wx(,%#:x1x2x3x4RHSx314∗1080x4230190z916000)2:5EXpE,x1,x2.j5Ex2pE,
"%1:EHx3ZE,%#9A:x1x2x3x4RHSx111020244x5∗0−3130444z50−40−320j5Ex1pE,
"%2:EHx4ZE,%#9A:

2、x1x2x3x4RHSx012−114255x10−3424155z00−1−4−440}V+D$+0,fz?',?'z:x2=14,x1=24,x3=x4=0,-%#?∗'6z=−440.P118ex1(2).:maxz=x1+3x2s.t.2x1+3x2+x3=6−x1+x2+x4=1xj≥0,j=1,2,3,4!"!>EX,X5Wx(,%#:x1x2x3x4RHSx323106x4−11∗011z−1−30008#zMAX,)2:5EXpE,x1,x2.j5Ex2pE,
"%2:EHx4ZE,

3、%#9A:x1x2x3x4RHSx35∗01−33x2−11011z−400331j5Ex1pE,
"%1:EHx3ZE,%#9A:x1x2x3x4RHSx101−331555x011282555z0043275553,x=8,x=x=0,(+zMAX,fz?',?'z:x1=52534-%#?'6z∗=27.5P119,ex3.:maxz=x1−3x2−x3s.t.3x1−x2+2x3+x4=7−2x1+4x2+x5=12−4x1+3x2+8x3+x6=10xj≥0,j=1,...,6!"!>EXx4,x5,

4、x6,X5Wx(,%#:x1x2x3x4x5x6RHSx43∗−121007x5−24001012x6−43800110z−13100008#zMAX,j5Ex1pE,
"%1:EHx4ZE,%#9A:x1x2x3x4x5x6RHSx1−12100713333x01042105053333x05324015863333z08510073333750588#zMAX,fz?',?'z:x1=3,x5=3,x6=3,x2=x3=x4=0,-%∗7#?'6z=3.P119ex1(5)#::minz=−3x1−x

5、2s.t.3x1+3x2+x3=304x1−4x2+x4=162x1−x2+x5=12xj≥0,j=1,...,5!"!>EX,X5Wx(,%#:x1x2x3x4x5RHSx33310030x44∗−401016x52−100112z3100002)2:5EXpE,x1,x2.j5Ex1pE,
"%2:EHx4ZE,%#9A:x1x2x3x4x5RHSx06∗1−301834x1−1010414x010−11452z040−30−124j5Ex2pE,
"%1:EHx3ZE,%#9A

6、:x1x2x3x4x5RHSx011−103268x101107168x00−1−311568z00−2−10−2434}V+D$+0,fz?',?'z:x2=3,x1=7,x5=1,x3=x4=0,-%∗#?'6z=−24.P119ex2(1)#::minz=4x1+6x2+18x3s.t.x1+3x3−x4=3x2+2x3−x5=5xj≥0,j=1,...,5%:ming=x6+x7s.t.x1+3x3−x4+x6=3+x2+2x3−x5+x7=5xj≥0,j=1,...,7%#:x1x2x3x4x5x6x7RHSx6103

7、−10103x70120−1015g00000−1−10s7,a7,E-%#}Æl0,~`,fE(DEU2)-%#}t.&-2a7,E-%#}k,"!#:x1x2x3x4x5x6x7RHSx6103∗−10103x70120−1015g115−1−1008)3:5EXpE,x1,x2,x3.j5Ex3pE,
"%13:EHx6ZE,%#9A:x1x2x3x4x5x6x7RHSx101−101013333x−21∗02−1−2137333g−2102−1