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Arnoff Enterprises manufactures the central processing unit (CPU) for a line of personal computers. The CPUs are manufactured in Seattle, Columbus and New York, and shipped to warehouses in Pittsburgh, Mobile, Denver, Los Angeles and Washington, D.C, for further distribution. The following transportation tableau shows the number of CPUs available at each plant and the number of CPUs required by each warehouse. The shipping costs (£ per unit) are also shown in each cell.
WarehousePlant Pittsburgh Mobile Denver Los Angeles Washington CPUsAvailableSeattle
9000Columbus
4000New York8000CPUs Required3000500040006000300021,000
a. Prepare an appropriate initial tableaub. Obtain an initial feasible solution using the least cost methodc. Proceed using the u, v method to determine the amount that should be shippedfrom each plant to each warehouse to minimise the total shipping cost.d. The Pittsburgh warehouse has just increased its order by 1000 units, and Arnoff has authorised the Columbus plant to increase its production by 1000 units. Will this lead to an increase or decrease in total shipping costs? Solve for the new optimal solution.
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