Use the following network representation of a transportation problem to answer the questions that follow:

x

i

j

$=$ number of units shipped from node

i

to node

j

$670$

$660$

$680$

$500$

$740$

$855$

$1$

$2$

$3$

A

B

C

$$9$

$$7$

$$7$

$$3$

$$9$

$$9$

$$9$

$$8$

$$5$

Supply

Demand

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In formulating an LP model for this network:

How many decision variables are required?

Besides non$-$negativity constraints, how many constraints are required?

The constraint for supply node $1$ is:

x

A

$1$

$+$

x

B

$1$

$+$

x

C

$1$

$=$

$670$

$9$

x

$1$

A

$+$

$7$

x

$1$

B

$+$

$7$

x

$1$

C

$=$

$670$

x

$1$

A

$+$

x

$1$

B

$+$

x

$1$

C

$<=$

$670$

$9$

x

$1$

A

$+$

$7$

x

$1$

B

$+$

$7$

x

$1$

C

$<=$

$670$

x

$1$

A

$+$

x

$1$

B

$+$

x

$1$

C

$=$

$670$

The constraint for demand node B is:

$7$

x

$1$

B

$+$

$9$

x

$2$

B

$+$

$8$

x

$3$

B

$<=$

$500$

x

B

$1$

$+$

x

B

$2$

$+$

x

B

$3$

$=$

$500$

x

$1$

B

$+$

x

$2$

B

$+$

x

$3$

B

$=$

$500$

x

$1$

B

$+$

x

$2$

B

$+$

x

$3$

B

$<=$

$500$

$7$

x

$1$

B

$+$

$9$

x

$2$

B

$+$

$8$

x

$3$

B

$=$

$500$