$($Study Yourself$)$ Consider the following network with unit delivery costs and the arc capacities given in the parentheses.

Nodes $1$ and $3$ have $5$ and $2$ units available, respectively. Nodes $2$ and $4$ need $3$ and $1$ units, respectively. Note that the problem is not in balance.

$($a$)$ What type of network problem is described above?

$($b$)$ Convert the network into a balanced network.

$($c$)$ To formulate an IP model for this problem,

Define all decision variables with the appropriate notation.

Write the objective $($maximize or minimize$)$ and the objective function.

Write all constraints in OPEN form.