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Question: a furniture manufacturer has three plants located in charlotte knoxville...

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A furniture manufacturer has three plants located in Charlotte, Knoxville, and Huntsville that need 500, 700, and 600 tons of lumber weekly, respectively. The manufacturer may purchase the lumber from three lumber companies headquartered in Asheville, Richmond, and Murfreesboro. The Asheville and Richmond lumber manufacturers have virtually unlimited supply, and because of other commitments, the Murfreesboro manufacturer cannot ship more than 500 tons each week. The Asheville lumber manufacturer uses rail for transportation, and there is no limit on the tonnage that it can ship to furniture facilities. On the other hand, the other two lumber companies use trucks that limit the maximum tonnage that can be shipped to any of the furniture companies to 200 tons. The table below gives the transportation cost from each lumber company to each furniture manufacturer (dollars per ton). Formulate (do not solve) the problem of satisfying furniture manufacturer demand as a linear programming problem.

Furniture

Lumber

Charlotte

Knoxville

Huntsville

Asheville

2

3

5

Richmond

2.5

4

4.8

Murfreesboro

3

3.6

3.2

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