Principles of Mathematics in Operations Research

272 Solutions

AUB = X =>AUB = X, AC\B = %=>B = (A)c

A and B are separated and A\J B = X => A = Bc

B is closed.

i.e. B is open.

so A is closed. Similarly,

10.4

Let

I

us place the origin at the lower left corner of the PCB. Then,

I |E i i i i i ,,

A =

l> =

(T' =

,/ =

hi

l

\°~

b

[6"

L

u

"8l

3

, B =

, E =

, H =

, K =

"1]

4

"Si

t\

("fi

[b

"ql

1

, c =

, F =

, / =

. L =

[91

2

Ml

4J

"7]

2

"ql

7

Use /i norm:

k A B C D E F G H I J K L

A B

0 3

3 0

2 3

6 3

8 5

6 3

6 9

9 6

7 8

9 8

8 11

CD EFGHIJK L

2 6 86 6979 8 14

3 3 53 9688 11 11

0 4 64 6757 8 12

4 0 24 10 599 12 8

6 2 04 10 599 12 6

4440635588

6 10 10 6 0 5 3 5 4 10

7553504475

5995340237

7995542035

8 12 12 8 4733 0 6

14 11 12 8 6 8 10 5 75 6 0

Nearest neighbor (in l\ metric):

intCK)B4 D(D or F) H-> E i-» F H> H

M- /(/ or J) H> J H->- if H-S- G »->• L h-> A

Initial tour length is 54. See Figure S.17.