Network flow problems

"Transportation Problems" are a subclass of network flow problems.

You have a set of source cities and a set of demand cities, the amount of supply in each source city, the amount of demand in each demand city, and the shipping costs for each (source,demand) city pair. You must exactly meet demand in each demand city, and each source city must ship out exactly what it produces (no more or less).

a) Formulate and solve a transportation problem as follows: Source cities: San Francisco and Los Angeles (SF and LA) Demand cities: Las Vegas and Phoenix (LV and Ph)

Costs: to: LV Ph
from SF 50 300
LA 320 60
(costs are per item shipped).
Supply: 5 in SF, 10 in LA
Demand: 7 in LV, 8 in Ph

Find the optimal shipping amounts and the total cost.
When Solver says it has a solution, ask it for the Sensitivity report as well, but don't look at it yet.

b) Add one unit of supply in SF and one unit of demand in Ph, re-solve, and report the new optimal decisions and total cost. Comment as appropriate.

c) Go back to the sensitivity report you generated in part (a) and look at the Lagrange Multipliers, and comment on them in relation to part (b).

d) In both (a) and (b), total supply and total demand matched each other perfectly. What would you do if supply exceeded demand? What if demand exceeded supply?