Consider the following maximal flow problem $($graph below$),$ we are interested in the

maximum number of cars per hour that can travel from node $1($origin$)$ to node $4$

$($destination$).$ The numbers in the circles indicate the node number $($i$.$e$.,$ node $1,$ node

$2,$ etc.$),$ arrows indicate the flow direction, the numbers above each arc give the upper

limits for each route $($maximum number of cars, in thousands$),$ the return arc $($from

node $4$ to node $1)$ has no upper limit$.$

Let $j$ be the number of cars moving from Node $i$ to Node $j.$

$($Description of the graph above: Node $1$ flows to Node $2$ with max $4$ cars$/$hr; Node $1$

flows to Node $3$ with max $5$ cars$/$hr; Node $2$ flows to Node $4$ with max $6$ cars$/$hr;

Node $3$ flows to Node $2$ with max $3$ cars$/$hr; Node $3$ flows to Node $4$ with max $2$

cars$/$hr$.$ Return arc from Node $4$ to Node $1.)$

Do NOT use summation notation, you will get an automatic $0$ for this question if you

do$!$

Answer the three $(3)$ questions below $($make sure to clearly mark the question $(1),(2),$

$(3)$ that you are answering$)$:

What is the objective function? Write it down.

What is the constraint for Node $1?$ Write it down. Make sure all the variables

$($X$)$ are on the left $($LHS$)$ and only constants are on the right $($RHS$).$

What is the constraint for Node $2?$ Write it down. Make sure all the variables

$($X$)$ are on the left $($LHS$)$ and only constants are on the right $($RHS$).$