Question

Find the shortest route from node 1 to node 7 in the network shown. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". For negative values enter "minus" sign (-). 17 1 19 Let Iijo 1 if the arc from node i to node j is on the shortest route otherwise + xz3 + | x25 + x12 + X32+ X 56 + X13+ x35+ C x57+ + C + x14 + X45+ C + + xs3 + : xs2 + C X67 + + s.t. Flow Out Flow In X13 + X14 Node 1 Node 2 + x25 + x12 + x13 + X32 + *23 + Node 3 X32 + X35 + Node 4 X46 + X52 + X53 + X56+ Node 5 *25+ X35 + + X65+ X57 + X56 Node 6 C Node 7 X45+ X57 + + X67 Xij 2 0 for all i and j

Answer 1

Answer:

Min = 11,12 +9:13 +19:14 +9:23 +11,25 +9:32 + 5.35 +18,46 +11,52 +5.53 + 20:56 +17:57 +20,65 +1767

using excel solver

SUM X fo =SUM(C12:112) D E B C F G H I LM 8 100 100 100 100 100 100 100 100 100 100 100 100 100 100 200 100 100 100 Total auawn www- 1 2 3 6 1 Total Out Out - In =SUM(C12:112) 0 0 0 0 0 o 0 = = Total In 0 O 0 0 0 0 0

Some of the values entered are dummy values. Values must be any between 100 or more.

SUM - X fx =SUM(C12:C18) D E B C F G H I J K L M 3 5 100 2 11 100 4 19 100 100 7 100 100 100 100 100 100 18 100 100 100 1 100 100 100 Total 7 Total Out Out - In 0 0 0 = Total In ESUM(C12:018) 0 0 0 0 0

SUM X fo=J12-C19 D E B C F G H I J K L M 23 4 5 9 100 100 100 100 100 i 100 Total 6 7 Total Out Out - In 0=312-014! 0 0 Total In 0 0 0 0 0

SUM A X L = SUMPRODUCT(C3:19,C12:118) D E F G B C H I J K L M N 3 4 5 7 1 100 2 119 6 100 100 100 9 100 100 9 100 100 100 100 100 100 100 100 100 100 100 Total =SUMPRODUCT(C3:19,C12:118)| 6 1 Total Out Out - In 0 = 0 = 0 0 0 0 0 0 0

Me Oyun Of To! O by Charynge $C$125B 100 100 le: 100 100 100 Sinct to the Congress 11 300 9 100 100 100 100 100 1005 100 100 100 100 $12 - 12 100 Change 20 100 100 100 100 100 100 1 100 7 100 100 Best A Meie Unconstaned Variables Monegative Select a Solving Method GRG Saling Method Select the CRG Miner egne for Solver des that are oth e r dette Simplex argne for new Scher Probleme, the y were for problems that за е а Total in

B C H 100 100 100 20 100 100 Total 6 7 Total Out Out - In 0 = 0 -1 = = 0 O 00 oo 1 Total In 1 0 1

Variable Value x12 0 x13 x14 x23 X25 x32 X35 x46 x52 x53 x56 x57 x65 X67

The shortest path is 1-3-5-7 and it takes 31 to complete