Question $4(45$ marks$)$:

Consider the following network.

Some nodes are demand nodes and the others are supply nodes. $($For example, node $1$ needs $3$ items so it

is a demand point. However, node $4$ supplies $5$ items so it is a supply node$)$

Demand nodes satisfy their demand by using their input flow. please reply example, if the input flow to node $1$ is $5,$

the output flow of node $1$ will be $5$ minus its demand$)$

Supply nodes provide their supply in their output flow. $($For example, if the input flow to node $4$ is $2,$ the

output flow of node $4$ will be $2$ plus its supply$)$

There is a shipment cost from each node to another node. $($For example, the shipping cost of $2$ items from

node $4$ to node $2$ is $2**3=6.)$

Each arc has a capacity. $($For example, the capacity of the arc from $4$ to $2$ is $3$ items. This implies that at

most $3$ items can be sent from node $4$ to node $2.)$

All demands must be satisfied, and the objective is to minimize the total shipping cost.

Formulate the problem as a Linear Program. $($NO NEED TO SOLVE IT$)$

All parameters can be found in the following tables. please reply fast its vey very urgent