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第一章 线性规划与单纯形法 PowerPoint PPT Presentation


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第一节 线性规划的基本概念 第二节 线性规划的标准形式和解的性质 第三节 单纯形法 第四节 人工变量法 第五节 线性规划应用举例. 第一章 线性规划与单纯形法. 通过本章的学习,要求学生掌握线性规划的图解法,深刻理解单纯形法的解题思路,熟练掌握其运算步骤,并能在实际问题中加以运用。. 本章学习目的和要求. 1 .已有一定数量的人力、物力、财力资源,研究如何充分合理地使用才能使完成的任务量最大。(如:利润、产值等最大。 maximum ) 2 .当一项任务量确定以后,研究如何统筹安排,才能使完成任务耗费的资源量为最小。(如:成本最小。 minimum ). 主要研究目的.

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第一章 线性规划与单纯形法

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1 maximum

2minimum


1-1 PQABC1-1


11

PQ


PQx1x2


A

B

20

10

40

0

0

20

/

2

2

3

1-2 3AB1-2

AB108


A

B

20

10

40

0

0

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3

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1-3 A1A23040B1B2B32025181-3/

B1

B2

B3

A1

A2

2

4

3

6

5

3


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1x1xn

2

3

Linear ProgrammingLP



1-1

1-2

1-3

x1x2xncjbi1-31-2aijx1xnRx1xn



X=x1x2xnT

C=c1c2cn

b=b1b2bmT

A=aijmn

Pj=a1ja2jamjT


n=2LP

1.

2.


1-4


x2

5

l2

4

Q4

Q3

l3

3

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Q1

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2

3

4

5

6

x1

1-1

1R

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2ZZ


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1.

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Q2Q3

X1+1X201X1+1X201


34X212Z

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x3x4x5

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1-9 LP


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XCbAPj=a1ja2jamjTxjAjA=P1P2Pn


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B=

0

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1

2

3

4

5

6

7

8

9

10

P1P2P3

P1P2P4

P1P2P5

P1P3P4

P1P3P5

P1P4P5

P2P3P4

P2P3P5

P2P4P5

P3P4P5

(14/53-4/500)T

(23040)T

(35/2002)T

(404012)T

(800-2012)T

(032140)T

(0-10-120-28)T

(04012-4)T

(0082012)T

Q3

Q2

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Q4

O

1-4


1R

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x3x4x5X1=(0,0,8,20,12)Tz1=0

1


z=2x1+5x2x1x2zx2x2zx2x1

x2min8/220/212/4=3

x5=0x5


1x2,x3,x4

2

X2=(0,3,2,14,0)Tz2=53=1515


2x2=3 x5z

z=2x1+5x2=2x1+53x5=2x1x5+15

x1x1x50

x1min2/114/5=2

x1=2x3=0x32x1x2x4

X3=(2,3,0,4,0)Tzz3=22+53=19

3


3x1=2x3+ x52

z=22x3+x5x5+15=2x3x5+19

z19X=X3z=19X3z19


1.


b1bm0X1=(b1,b2,,bm,0,,0)T

i=12m


0

xjjxjzj>0xj


1-5

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Xxi=bii=1mxj=0

CBb

xjjcjCBxj


1

X1j0X1

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xk


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xk

xl


4

alk10l1/alklaik/alkii=12mil


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LP


1.

X1

1j0xk02j<0


LP


X1xkk>0aik0i=12mxk

2.


z1=zmax z1

j0

xk

3. min z



M

1-15 LP


x4x5LPP1

x6x7


P1

P2


X=(x1x2x3x4x5)TXA=(x6x7)T

1P1X*X*XA*=0P2

2P2X*XA*=0X*P1P2XA*0P1


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