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HW5 solutions

# HW5 solutions - =-1 = = = = = = 1 Problem 5-16 see network...

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Problem 5-5 p. 222 1 2 3 4 5 -5 -7 +0 +4 +8 7 6 4 5 8 9 3 5

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Problem 5-14 p. 225 a) b) c) X12 X13 X15 X17 X23 X24 X25 X27 X34 X35 DV 0 1 0 0 0 0 0 0 0 0 OF 5 13 45 105 27 19 50 95 14 30 C1 -1 -1 -1 -1 C2 1 -1 -1 -1 -1 C3 1 1 -1 -1 C4 1 1 C5 1 1 1 C6 C7 1 1 San Diego LA 2 1 Denver 3 St Lou 4 Chic. 6 Memp 5 NY 7 -1 +1 5 13 45 105 27 19 50 95 14 30 32 14 35 24 35 18 25 24 18 17 MIN 5 X12 + 13 X13 + 45 X15 + 105 X17 + 27 X23 + 19 X24 + 50 X25 + 95 X27 + 1 + 14 X43 + 35 X45 + 24 X46 + 35 X54 + 18 X56 + 25 X57 + 24 X64 + 18 X65 + 17 Subject to the constraints -X12 - X13 - X15 - X17 = -1 +X12 - X23 - X24 - X25 - X27 = 0 +X13 + X23 + X43- X34 - X35 - X36 = 0 +X24 + X34 + X54 + X64 - X43 - X45 - X46 = 0 + X15 + X25 + X35 + X45 + X65 - X54 - X56 - X57 = 0 + X36 + X46 + X56 - X64 - X65 - X67 = 0 + X17 + X27 + X57 + X67 = +1 X ij >= 0 The least costly route is X1 - X3 - X6 - X7 at a total cost of 62. (San Diego to Den San Diego LA 2 1 Denver 3 St Lou 4 Chic. 6 Memp 5 NY 7 -1 +1 5 13 45 105 27 19 50 95 14 30 32 14 35 24 35 18 25 24 18 17
X36 X43 X45 X46 X54 X56 X57 X64 X65 X67 1 0 0 0 0 0 0 0 0 1 Min 32 14 35 24 35 18 25 24 18 17 62 -1 0 -1 1 0 -1 -1 -1 1 1 0 1 -1 -1 -1 1 0 1 1 1 -1 -1 -1 0 1 1 1 14 X34 + 30 X35 + 32 X36 7 X67 nver to Chicago to New York)

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Unformatted text preview: =-1 = = = = = = 1 Problem 5-16 see network diagram on p. 226 X13 X14 X23 X24 X34 X35 X36 X43 DV 1300 1100 800 OF 3 4 3 4 7 9 6 7 NODE 1-1-1 NODE 2-1-1 NODE 3 1 1-1-1-1 1 NODE 4 1 1 1-1 NODE 5 1 NODE 6 1 NODE 7 DV: X13, X14, X23, X24, X34, X35, X36, X43, X46, X47, X56, X67 OF: MIN 3X13+4X14+3X23+4X24+7X34+9X35+6X36+7X43+4X46+8X47+3X56 +2X67 ST: (note total supply exceeds total demand) NODE 1: -1300 <= -X13-X14 NODE 2: -1200 <= -X23-X24 NODE 3: 300 <= X13+X23+X43-X34-X35-X36 NODE 4: 200 <= X14+X24+X34-X43-X46-X47 NODE 5: 800 <= X35-X56 NODE 6: 700 <= X36+X46+X56-X67 NODE 7: 400 <= X47+X67 ALL Xij >= 0 X46 X47 X56 X67 1100 400 MIN 4 8 3 2 20900-1300 >=-1300-1100 >=-1200 300 >= 300-1-1 200 >= 200-1 800 >= 800 1 1-1 700 >= 700 1 1 400 >= 400...
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