運籌學(胡運權)第五版課后答案,運籌作業(yè)

1、47頁1.1b1 2 3 44321X12x1+x2=23x1+4x2=120X2用圖解法找不到滿足所有約束條件的公共范圍，所以該問題無可行解47頁1.1d1 2 3 454321-1-2-6 -5 -4 -3 -2 -1X2X12x1-x2=2-2x1+3x2=2無界解)(1.2（b）約束方程的系數(shù)矩陣 A= 1 2 3 4 2 1 1 2 P1 P2 P3 P4基基解是否可行解目標函數(shù)值X1 X2 X3 X4P1 P2-4 11/2 0 0否P1 P32/5 0 11/5 0是43/5P1 P4-1/3 0 0 11/6否P2 P30 1/2 2 0是5P2 P40 -1/2 0 2否P3

2、 P40 0 1 1是5最優(yōu)解A=(0 1/2 2 0)T和(0 0 1 1)T49頁13題設Xij為第i月租j個月的面積minz=2800x11+2800x21+2800x31+2800x41+4500x12+4500x22+4500x32+6000x13 +6000x23+7300x14s.t. x11+x12+x13+x1415 x12+x13+x14+x21+x22+x2310 x13+x14+x22+x23+x31+x3220 x14+x23+x32+x4112 Xij0用excel求解為：用LINDO求解： LP OPTIMUM FOUND AT STEP 3 OBJECTIVE

3、FUNCTION VALUE 1) 118400.0 VARIABLE VALUE REDUCED COST Z 0.000000 1.000000 X11 3.000000 0.000000 X21 0.000000 2800.000000 X31 8.000000 0.000000 X41 0.000000 1100.000000 X12 0.000000 1700.000000 X22 0.000000 1700.000000 X32 0.000000 0.000000 X13 0.000000 400.000000 X23 0.000000 1500.000000 X14 12.000

4、000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 -2800.000000 3) 2.000000 0.000000 4) 0.000000 -2800.000000 5) 0.000000 -1700.000000 NO. ITERATIONS= 3答 若使所費租借費用最小，需第一個月租一個月租期300平方米，租四個月租期1200平方米，第三個月租一個月租期800平方米，50頁14題設a1，a2，a3, a4, a5分別為在A1, A2, B1, B2, B3加工的產品數(shù)量，b1，b2，b3分別為在A1, A2, B1加工的產

5、品數(shù)量，c1為在A2，B2上加工的產品數(shù)量。則目標函數(shù)為maxz= (1.25-0.25)( a1+a2+a3)+( 2-0.35) b3+( 2.8-0.5)c1 -0.05 (a1+b1)- 0.03 (a2+b2+c1)- 0.06 (a3+b3)-0.11(a4+c1)-0.05a5=0. 95a1+0. 97a2+0. 94a3+1.5b3+2.1c1-0.05b1-0.11a4-0.05a5s.t. 5a1+10b16000 7a2+b2+12c110000 6a3+8a34000 4a4+11c17000 7a54000 a1+a2-a3-a4-a5=0 b1+b2-b3=0 a

6、1，a2，a3, a4, a5, b1，b2，b3, c10用lindo求解得：LP OPTIMUM FOUND AT STEP 6 OBJECTIVE FUNCTION VALUE 1) 16342.29 VARIABLE VALUE REDUCED COST A1 1200.000000 0.000000 A2 0.000000 9.640000 A3 285.714294 0.000000 B3 10000.000000 0.000000 C1 0.000000 15.900000 B1 0.000000 0.230000 A4 342.857147 0.000000 A5 571.42

7、8589 0.000000 B2 10000.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.168000 3) 0.000000 1.500000 4) 0.000000 0.075000 5) 5628.571289 0.000000 6) 0.000000 0.008571 7) 0.000000 0.110000 8) 0.000000 -1.500000 NO. ITERATIONS= 6計算lindo截屏2.1a:對偶問題為：maxz=2y1+3y2+5y3s.t. y1+2y2+y32 3y3+y2+4

8、y32 4y1+3y2+3y3=4y10, y 20,y3無約束因為原問題的對偶問題的對偶問題仍是原問題，因此本問題的對偶問題的對偶問題為：minz=2x1+2x2+4x3s.t. x1+3x2+4x322x1+x2+3x33x1+4x2+3x3=5x1,x20,x3無約束81頁2.12a)設x1,x2,x3分別為A，B，C產品數(shù)量maxz=3x1+x2+4x3s.t.6x1+3x2+5x3453x1+4x2+5x330x1,x2,x30用lomdo求解為LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 1) 27.00000 VARIAB

9、LE VALUE REDUCED COST X1 5.000000 0.000000 X2 0.000000 2.000000 X3 3.000000 0.000000 X1,X2,X3 0.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.200000 3) 0.000000 0.600000 4) 0.000000 0.000000 NO. ITERATIONS= 2最大生產計劃為A生產5個單位，C生產3個單位b) LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALU

10、E 1) 27.00000 VARIABLE VALUE REDUCED COST X1 5.000000 0.000000 X2 0.000000 2.000000 X3 3.000000 0.000000 X1,X2,X3 0.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.200000 3) 0.000000 0.600000 4) 0.000000 0.000000 NO. ITERATIONS= 2 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIEN

11、T RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 3.000000 1.800000 0.600000 X2 1.000000 2.000000 INFINITY X3 4.000000 1.000000 1.500000 X1,X2,X3 0.000000 0.000000 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 45.000000 15.000000 15.0000

12、00 3 30.000000 15.000000 7.500000 4 0.000000 0.000000 INFINITY可知A產品的利潤變化范圍【6. 8,2.4】,上述計劃不變。c)設x4為產品D的數(shù)量maxz=3x1+x2+4x3+3x4s.t.6x1+3x2+5x3+8x4453x1+4x2+5x3+2x430x1,x2,x3 ,x40用lomdo求解為 LP OPTIMUM FOUND AT STEP 0 OBJECTIVE FUNCTION VALUE 1) 27.50000 VARIABLE VALUE REDUCED COST X1 0.000000 0.100000 X2

13、0.000000 1.966667 X3 5.000000 0.000000 X4 2.500000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.233333 3) 0.000000 0.566667 NO. ITERATIONS= 0安排生產D有利，新最有生產計劃為x1=x2=0,x3=5,x4=2.5，利潤為27.5d)maxz=3x1+x2+4x3-0.4ys.t. 6x1+3x2+5x345 3x1+4x2+5x3-y30 x1,x2,x3,y0用lomdo求解為 LP OPTIMUM FOUND AT STEP 0

14、OBJECTIVE FUNCTION VALUE 1) 30.00000 VARIABLE VALUE REDUCED COST X1 0.000000 0.600000 X2 0.000000 1.800000 X3 9.000000 0.000000 Y 15.000000 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.400000 3) 0.000000 0.400000 NO. ITERATIONS= 0可知購進原材料15個單位為宜。4.1a）設yi= 1 第i組條件起作用0 第i組條件不起作用x1+x22-(1-y1)

15、M M 充分大正數(shù)2x1+3x25+(1-y2)My1+y2=1y1,y2=0或1b)設yi= 1 第i組條件起作用0 第i組條件不起作用 x=0y1 x=3y2 x=5y2 x=7y4 y1+y2+y3+y4=1 y1,y2,y3,y4=0或1c) 設yi= 1 為假定取值500 為假定取值x=0 x=0y1x50-(1-y2)M y1+y2=1y1,y2=0或1d) 設yi= 1 第i組條件起作用 0 第i組條件不起作用 i=1,2 則x12+(1-y1)Mx21-(1-y1)Mx24+(1-y2)My1+y2=1y1,y2=0或1e) 設yi= 1 第i組條件起作用 0 第i組條件不起作

16、用 i=1,2 則x1+x25-(1-y1)Mx12-(1-y2)Mx32+(1-y3)Mx3+x46+(1-y4)My1+y2+y3+y42y1,y2,y3,y4=1或04.2minz=j=110cjxj j=110xj=5 x1+x8=1 x7+x8=1s.t. x3+x51 x4+x51 x5+x6+x7+x82 xj= 1 選擇鉆探第sj井位 0 否4.5設xij為第i種泳姿用第名運動員minz=i=14j=15aijxijs.t.x11+x12+x13+x14+x15=1 x21+x22+x23+x24+x25=1 x31+x32+x33+x34+x35=1 x41+x42+x43+x44+x45=1 x11+x21+x22+x23=1x12+x22+x32+x42=1x13+x23+x33+x43=1x14+x24+x34+x44=1x15+x25+x35+x45=1xij=1或0（i=1,2,3,4 j=1,2,3,4,5