$1.$ Solve the shortest route problem.

You are a student on vacation in London. You are trying to save money, so you are using the "tube" to get around. You found an inexpensive place to stay at Liverpool Street. Today you are touring Westminster and want to find the quickest route there. Do not consider the maroon, orange, and pink routes that leave Liverpool heading west or the black line that heads south from Moorgate. Only consider the connecting stations such as Bank, Holborn, Leicester Square, etc.

London's 'walk the Tube' map reveals the real distance between stations $-$ The Verge

I have added up the times between stations and color$-$coded the names to the tube lines.

X $1234567891011121314$

X Liverpool Street Bank Holborn Tottenham Court Road Oxford Circus Bond Street Leicester Square Piccadilly Circus Green Park Victoria Monument Embankment Charing Cross Westminster

$1$ Liverpool Street

$2$ Bank $10$

$3$ Holborn $31$

$4$ Tottenham Court Road $10$

$5$ Oxford Circus $9$

$6$ Bond Street $7$

$7$ Leicester Square $128$

$8$ Piccadilly Circus $126$

$9$ Green Park $15148$

$10$ Victoria $19$

$11$ Monument $15$

$12$ Embankment $383$

$13$ Charing Cross $7113$

$14$ Westminster $211110$

Hint: look at how a transshipment was modeled and the formulation on page $447$ Figure $10\mathrm{.}14$

$2.$ Solve the maximal flow problem.

As you can see the natural gas shipping problem is complex in the US$.$ It comes in from several ports $($mainly Canada and Louisiana$)$ and goes all over.

A map of the US with the natural gas flow shown in red arrows.

Let's make this smaller since this is only a class homework. Take the following map.

Let's say that the gas comes into NY and flows to SoCal using these $8$ nodes.

I am providing you the flow maximum tables.

Bi$-$directional flow is allowed.

What is the optimal route to maximize the flow to SoCal $($X$81)?$

A map of the US with the different natural gas trading points located on it to show there relative physical relationships to each other.

Transco Appalachia Henry Houston El Passo Rockies PG&E SoCal

Transco

Appalachia $6$

Henry $65$

Houston $61$

El Passo $733$

Rockies $864$

PG&E $5$

SoCal $543$

please use excel AND solver