Solve the below problem:
Formulate as a Linear Program and then solve using Lingo or Excel Solver
Q: A furniture manufacturer has three plants that need 500, 700, and 600 tons of lumber weekly. The manufacturer may purchase the lumber from three lumber companies. The first two lumber manufacturers virtually have an unlimited supply and, because of other commitments, the third manufacturer cannot ship more than 500 tons weekly. The first lumber manufacturer uses rail for transportation and there is no limit on the tonnage that can be shipped to the furniture facilities. On the other hand, the last two lumber companies use trucks that limit the maximum tonnage that can be shipped to any of the furniture companies to 200 tons. The following table gives the transportation cost from the lumber companies to the furniture manufacturers per ton)
LUMBER COMPANY FURNITURE FACILITY
1 1 2 3
2 1 3 5
3 3.5 4 4.8
3.5 3.6 3.2