Formulate and solve a linear program to determine the shipping arrangements (mode, destination, and quantity) that will minimize the total shipping cost.
1. Transportation Problem:
The Navy has 9,000 pounds of material in Albany, Georgia that it wishes to ship to three
installations:
San Diego, Norfolk, and Pensacola.
They require 4,000, 2,500, and 2,500 pounds, respectively (Destination or Demand
amounts). Government regulations require equal distribution of shipping among the three
carriers (Supply nodes).
Note: This means the supply is the same for each type of
transportation.
The shipping costs per pound for truck, railroad, and airplane transit are shown below.
Formulate and solve a linear program to determine the shipping arrangements (mode,
destination, and quantity) that will minimize the total shipping cost.
Destination
Mode San Diego Norfolk Pensacola
Truck $12 $ 6 $ 5
Railroad 20 11 9
Airplane 30 26 28
2. Transshipment Problem
The Northside and Southside facilities of Zeron Industries supply three firms (Zrox,
Hewes, Rockrite) with customized shelving for its offices. They both order shelving
from the same two manufacturers, Arnold Manufacturers and Supershelf, Inc.
Currently weekly demands by the users are 50 for Zrox, 60 for Hewes, and 40 for
Rockrite. Both Arnold and Supershelf can supply at most 75 units to its customers.
Because of long standing contracts based on past orders, unit costs from the
manufacturers to the suppliers are:
Zeron N Zeron S
Arnold 5 8
Supershelf 7 4
The costs to install the shelving at the various locations are:
Zrox Hewes Rockrite
Zeron N 1 5 8
Zeron S 3 4 4
How should Zeron ship to minimize their costs?
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