Problem

$1$

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$($

$1$

$1$

pts

$)$

A beer distributor needs to plan how to make deliveries from its warehouse

$($

Node

$1$

$-$

origin

$/$

start

$)$

to a supermarket

$($

Node

$7$

$-$

destination

$/$

terminal node

$)$

$,$

as shown in the network below. All the roads allow for bi

$-$

directional traffic

$($

e

$.$

g

$.$

$,$

you can go from Node

$3$

to Node

$4$

and from Node

$4$

to Node

$3$

$)$

$.$

The numbers above each arc

$($

road

$)$

denote length of road in miles

$($

in either direction

$)$

$.$

The distributor is looking to find the shortest route from the warehouse to the supermarket. Let

$=$

$1$

if you take the road from Node i to Node

$,$

$=$

$0$

if not. Write down the following constraints: a

$.$

Constraint for Node

$1$

$($

origin

$/$

start node

$)$

$.$

b

$.$

Constraint for Node

$7$

$($

destination

$/$

terminal node

$)$

$.$

c

$.$

Constraint for Node

$4$

$.$

d

$.$

Constraint for Node

$5$

$.$