SOLUTIONS MANUAL for Operations Research An Introduction 10th Edition by Hamdy Taha

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Chapter 1

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Chapter 1 1 Chapter

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Chapter 1

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 2

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Chapter 3

Chapter 3

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Chapter Chapter 33

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 4

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 5

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

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Chapter 6

Chapter 6

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Chapter 6

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 7

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 9

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Chapter 10

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Chapter 10

Chapter 10

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Chapter 10

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Chapter 10

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Chapter 10

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Chapter 10

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Chapter 11

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Chapter 11 6 (a) Add a fictitious site (#9) to account to for the open tour. The cost to and from city 9 is zero. param d: 1 2 3 4 5 6 7 8 9:= 1 . 20 30 25 12 33 44 57 0 2 22 . 19 20 20 29 43 45 0 3 28 19 . 17 38 48 55 60 0 4 25 20 19 . 28 35 40 55 0 5 12 18 34 25 . 21 30 40 0 6 35 25 45 30 20 . 25 39 0 7 47 39 50 35 28 20 . 28 0 8 60 38 54 50 33 40 25 . 0 9 0 0 0 0 0 0 0 0 . ; (b) Using amplAssignment.txt: Lower bound on cab fare = $125 > budgeted amount.

Using amplLP-LB.txt will provide a (trivial) zero lower bound because the TSP is open tour.

7 (a) Each project represents a city. The table below gives the number of distinct employees who enter/leave the manager’s office when we switch from project i to project j (i.e., the number of mismatched “x” between column i and column j). The objective is to find a “tour” through all projects that will minimize the total traffic. “Project” 7 is added to account for the open tour.

1 1 2 3 4 5 6 7

4 4 6 6 5 0

2 4 6 4 6 3 0

3 4 6 4 8 7 0

4 6 4 4 6 5 0

5 6 6 8 6 5 0

6 5 3 7 5 5

7 0 0 0 0 0 0

0

(b) Lower bound using amplAssignment.txt is 20. Although the lower bound happened to be exactly equal to the true minimum tour, the associated assignment solution includes sub-tours; namely, 1-3-4-1, 2-6-2, 5-7-5.

8 (a) Set all entries tj1 = 0 for j = 2, 3, …, 8 (b) Using amplAssignment.txt: Lower bound = 25 minutes, sub-tour solution 1-4-1, 2-7-2,3-5-3, 6-8-6. (c) Lower bound on optimal tour = 25 minutes. 20 min windows is impossible to satisfy.

9 Assignment solution: 1-3-1, 2-5-2, 4-6-4, length = 8.6 mm Lower bound on time per board= 8.6/7 + 6x.5=4.23 sec Lower bound on production rate per hour = 3600/4.23= @851 boards per hour

10 (a) String = city, distance = overlap length. (b) Using amplAssignment.txt: Lower bound is 8 with sub-tours 1-3-1, 2-5-4-6-2

11 (a) Object = city, fuel consumption = distance. (b) Use amplAssignment.txt and amplLP-TSPLB.txt. Assignment LB = 14.7, subtour solution 1-3-2-1, 4-5-6-4, LP-LB = 14.1.

Associated cost = 14.1x12 = $169.20

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Chapter 11

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Chapter 11

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Chapter 11

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Chapter 11

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 12

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Chapter 13

See file ampl13-18.txt.

Modify K1 to K5: 35, 28, 30, 25, 20

18

AMPL model will not converge unless KiDi/yi is replaced with KiDi/(yi+ε), where ε>0 and very small.

SOLUTION: Total cost = 568.11 y1 = 4.42 y2 = 6.87 y3 = 4.12 y4 = 7.20 y5 = 5.80 ____________________________________________

See file ampl13-19.txt.

19

New constraint: (1/2)(y1 + y2 + y3) ≤ 25 SOLUTION: Total cost = 10.42 y1 = 10.83 y2 = 16.85 y3 = 22.32 _____________________________________________ See file ampl13-20.txt.

New constraint: Average inventory for item i = yi /2.

(1/2)(100y1 + 55y2 + 100y3) ≤ 1000

20

SOLUTION: Total cost = 14.31 y1 = 5.58 y2 = 7.90 y3 = 10.07 _____________________________________________ See file ampl13-21.txt.

21

AMPL model will not converge unless KiDi/yi is replaced with KiDi/(yi+ε), where ε>0 and very small.

New constraint: 365(10/y1 +20/y2 + 5/y3 + 10/y4) ≤ 150 SOLUTION: Total cost = 54.71 y1 = 155.30 y2 = 118.81 y3 = 74.36 y4 = 90.09

13-7

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Chapter 15

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Chapter 15

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Chapter 15

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Chapter 16

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Chapter 17

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

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Chapter 18

Chapter 18

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Chapter 18

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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Chapter 19

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© 2017 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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Chapter 20

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© 2017 Pearson Education, Inc., Hoboken, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Chapter 21

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Chapter 21

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Chapter 21

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Chapter 21

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Chapter 21

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Chapter 21

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Chapter 21

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Chapter 21

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21-10

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Appendix C

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Appendix C

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Appendix C

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Appendix C

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Appendix C

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Appendix C

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ERRATA Taha, operations research 10th ed (US edition) 8/6/16 p. xxxv, 4th line from bottom: Karen Standly → Karen Standley p. 636, 9th line from bottom: a (LIFO → a LIFO p. 403, Problem 10-29: Repeat Problem 5 → Repeat Problem 10-28 p. 404, Problem 10-42: Repeat Problem 1 → Repeat Problem 10-41 p. 768, Problem 2-22, bottom line: 31, 68 → 31.68 p. 788, Problem 11-2, Minimize z → Maximize z

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