BÀI TOÁN QUY HOẠCH TUYẾN TÍNH

§ 0.06kg 0.08kg 0.04kg x1; x2 ; x3 xi  0, i  1,3 0.06 x1  0.04 x2  0.07 x3 0.08x1  0.x2  0.04 x3 x1  1.7 x2  1.8x3 1 f  x   x1  1.7 x2  1.8 x3  max 2 0.06 x1  0.04 x2  0.07 x3  500   0.08 x1  0.x2  0.04 x3  300 3 x j  0, j  1.3 0.06 0.04 0.07 A 0.04 0.08 -1- 0.07kg 0.04kg 500 B  300 x  x1; x2 ; x3  x  x1; x2 ; x3  x  x1; x2 ; x3  p2 p3 XN 3.5m 2.8m 20h 4m 10h 2.6m 16h 3.8m 12h 2.5m 1) x1; x2 ; x3 x j  0, j  1,3 2) 3) 35x1  40 x2  43x3 , 45x1  42 x2  30 x3 , 45x1  42 x2  30 x3  35x1  40 x2  43x3  10 x1  x2  13x3  35x1  40 x2  43x3 , 4) -2- 18h 15h 5) 3.5  35x1   40x2  3.8  43x3  2.8  45x1  2.6  42x2  2.5  30x3 248.5 x1  269.2 x2  238.4 x3 20  35x1  16  40x2  18  43x3  10  45x1  12  42x2  15  30x3 1150x1  1144x2  1224x3 x1  x2  x3 1 f x   x1  x2  x3  10 x1  x2  13x3    35 x1  40 x2  43x3  1500 2 248.5 x1  269.2 x2  238.4 x3  10000  1150 x1  1144 x2  1224 x3  52000 3x j  0, j  1,3  13   10    35  1500  40 43     A , B 248.5 269.2 238.4 10000       1150 1144 1224  52000 C2, C3 -3- 1, CT km Kho C1 C2 C3 15T 20T 25T km 5km K1 20T 4km x11 2km x12 3km 6km x13 K2 40T x22 x21 - x23 T  km xij i  1,2; j  1,2,3 Ki  C j xij  x11  x12  x13 x21  x22  x23 x11  x21 x12  x22 2 x13  x23 T  km : 5x11  x12  x13  x21  3x22  x23 -4- 1 f x   x11  x12  x13  x21  3x22  x23   x11  x12  x13  20  x  x  x  40 22 23  21 2 x11  x21  15  x  x  20 12 22   x13  x23  25 3xij  i  1,2; j  1,2,3 -5- § t: n 1 f x    c j x j  max  j 1  n   aij x j  bi  j 1  n 2  aij x j  bi  j 1  n   aij x j  bi  j 1 3x j   j  J1 ; x j   j  J ; x j tu  y - Vector x  x1; x2 ;; xn  - y   j  J ; J1  J  J  1;2;; n - 1 f x   3x1  x2  x3  x4  x5  max 2 x1  x2  x3  x4  x5  17  x1  x2  x3  20 2  x1  x2  x3  x5  18  x1  x2  x3  x4  100 3x1; x4  0; x2 ; x5  0; x3 tu  y y n 1 f x    c j x j  max  j 1 n 2  aij x j  bi j 1 i  1, m 3x j   j  1, n  -6- 1 f x   3x1  x2  x3  3x4  x5   x1  x2  x3  3x4  2 x2  x3  x4  x5  18  x  x  x  17  3x j  0; j  1,5 n 1 f x    c j x j  max  j 1  x1  2    a1m 1 xm 1   a1n xn  b1  a2m 1 xm 1   a2n xn  b2 x2  xm  amm 1 xm 1   amn xn  bm 3x j   j  1, n ; bi  0i  1, m  x1 x2 xm xm 1 xn  a1m 1 a1n    a a   m  n  A            0 a a  mm 1 mn      bi  i  1, m x1; x2 ;; xm - x1; x2 ;; xm ; xm1;; xn   b1; b2 ;; bm ;0;;0 -7- bi  0, i  1, m 1 f x   3x1  x2  x3  3x4  x5   x1  x4  x5  20 2 3x1  x2  x4  x6   x  x  x  x  28  3x j  0; j  1,6 x1 x2 x3 x4 x5 x6  0 0   A    1  0   x1, x2 , x3, x4 , x5 , x6,   0,0,28,0,20,0 -8- §3 n  aij x j  bi j 1 xi 1  n  aij x j  xn 1  bi j 1 n  aij x j  bi j 1 xi 1  - n  aij x j  xn 1  bi j 1 x j  ta thay x j  t j , t j  x j tu  y y ta thay x j  xj  xj , xj , xj  : 1 f x   x1  x2  x3  x4  x5   x1  x2  x3  x4  x5   x1  x2  x3  x4  x5  7a    x2  x3  x4  1  x2  x3  x4  1b    2  x3  x4  3x5  10 x3  x4  3x5  10c     x1  x2  x3  x4  20  x1  x2  x3  x4  20d  3x1; x5  0; x4  0; x2 ; x3 tu  y y  x6  x7    -1 x8   Thay x4  t4 ; t4   Thay x2  x2  x2 ; x2  x2   Thay x3  x3  x3 ; x3  x3  -9- 1 f x   x1  x2  x2   2x3  x3   t  x5  0.x6  x7  x8   x1  2 x2  x2    x3  x3   2t  x5  x6  7a     x2  x2   2 x3  x3   t  x7  1b  2 2 x3  x3   t  3x5  x8  10c    x1   x2  x2   2 x3  x3   t  20d  3x1; x5  0; t  0; x2 ; x2 ; x3 ; x3 ; x6 ; x7 ; x8  x10 , x20 , x20 , x30 , x30 ,t40 , x50 , x60 , x70 , x80  x10 , x20 , x30 , x40 , x50 with x20  x20  x20 , x30  x30  x30 , x40  t40 bi  0, i  1, m ) n 1 f x    c j x j  max  j 1 a11 x1    a1n x n  b1 a x    a x  b 11 2 11    a11 x1    a11 x1  bm 3x j   j  1, n  xn i    f x    f x   max - 10 - –M f x   1040 10 10 10 20 20 5 15 20 30 11 10 5 15 20 10 30 S=-5 10 10 4 1 20 7 -1 R=2 (+5) R=2 11 R=0 5(-5) 0 0 10 10 S=-5 S=-3 V  2,5, 2,4, 4,4, 4,5, 20,5  - 73 - 20 5(+5) S=-9 20(-5) S=-11 R=4 10 6 au: 2 R=1 R=0 11 R=0 0 0 10 10 S=0 S=-1 10 S=0 S=0 R=0 15 S=0 0 0 10 X  0  0 0 0 5  10 10   10 15 0 f x   435 sau: 30 15 15 25 15 40 - 74 - 30 25 15 5 40 15 2 20 -1 R=0 (+15) 3 15(-15) 25 S=-2 15 0(+15) S=-1 15(-15) S=-3 S=-1 - V  2,4, 2,2, 3,2, 3,4, 15,15  15 5 25 S=0 0 2 R=0 20 R=0 15 R=0 15 S=0 S=1 S=0 0  20  X   0 15   25 15 0  f x   150 - 75 - R=-1 R=0 6) 180 200 230 280 280 14 320 290 180 280 200 320 0 290 180 5 230 -1 200 S=-3 S=0 14 140 280 7 R=-3 280 R=-2 90 S=-4 - S=-4 V  2,2, 3,2, 3,3, 2,3, 200,140  140 0 180 S=-1 140 60 S=0 14 7 R=0 R=1 280 0 230 S=0 S=0 0 - 76 - R=0 R=0 0 280  X  180 140 0     60 230  f x   3980 12 15 10 12 19 11 9 10 19 11 (+6) 8(-6) S=-7 -3 12 6(-6) 1(+6) S=-8 12 15 12 6 S=-5 11 S=-5 V  2,1, 4,1, 4,2, 2,2, 6,8  au: - 77 - 0 0 R=0 R=4 R=6 S=0 R=0 4 9 2 S=3 12 12 7 S=3 11 S=0 S=0 0 R=0 0 R=0 R=0 R==-3 S=0 0 0 6 X  0  2 6 12 1  0 11 0  0 0 f x   131 8) 20 50 60 30 50 40 70 11 - 78 - 20 50 50 60 30 0 10 R=10 50 40 -1 R=4 70 20 20(-10) (+10) 11 0 30(+10) S=-7 S=-6 10(-10) S=-11 30 S=0 V  2,3, 2,2, 3,2, 3,3, 10,20  10 7 0 50 0 R=0 0 20 10 10 11 S=0 40 S=0 S=1  0 50  X  20 10 10     40 30 0 u: R=-1 30 S=0 f x   460 - 79 - R=0 R=0 9) 30 40 60 70 100 80 20 30 100 40 80 20 30 60 20 70(-30) -1 R=0 30(-30) (+30) S=-6 S=-5 V  2,4, 1,4, 1,3, 2,3, 70,30  30 (+30) -1 30(-30) 20 S=0 20 S=0 60 0 R=3 30(+30) 20 S=-3 S=-7 70 40(-30) R=0 30(+30) R=0 S=1 S=1 V  1,1, 2,1, 2,4, 1,4, 40,30  30 - 80 - R=-1 -1 R=1 30 20 S=1 60 0 20 S=0 S=0 30 60 10  X   20 60    20 0  R=0 10 R=0 60 R=0 S=0 0 f x   660 10 150 120 80 50 100 11 130 170 12 150 120 100 130 20(-20) 170 130 5 50 -2 11 R=3 80(+20) -1 R=5 12 0 R=0 -1 (+20) S=-6 80 40(-20) S=-8 80 S=-12 V  3,1, 3,2, 1,2, 1,1, - 81 - 50 S=-7 40,20  20 130 -2 11 R=0 100(-80) (+80) -2 R=-1 12 0 R=0 20 S=1 0 20(+80) S=0 80(-80) S=0 50 S=0 V  1,3, 1,2, 3,2, 3,3, 100,80  80 130 20 S=0 11 R=0 20 80 R=0 12 R=0 100 S=0 20 80   X  130 0 0    20 100 50 S=2 50 S=0 0 f x   2040 - 82 - 1) 25 40 20 10 40 20 35 25 15 0  X   0 20     25 10 f x   340 2) 220 310 200 250 300 500 12 11 13 180 10 15 18 14 50 250  X   40 260 200    180 0  f x   8690 - 83 - 3) 76 62 88 45 40 79 10 19 102 13 11 70 12 17 10 60 12 18 18  31 48 0   62 40 0   X   0 30 40   45 0 15  f x   2659 4) 85 75 60 105 16 10 50 14 65 10 18 12 20 55 14 18 45 8 12 85 0 20  0 60   X   55 0     20 25 f x   2080 - 84 - 5) 120 280 130 270 100 300 10 11 150 10 250 12 13 100    30 270  X  120 30 0      220 30 f x   5590 - 85 - -2003 -2004 2007 - 86 - Trang 1 15 15 20 26 41 41 44 47 59 59 61 66 68 86 87 § §2 § §1 § § § § § §3 : - 87 -