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.
Warehouse
Plant Pittsburgh Mobile Denver Los Angeles Washington CPUs
Available
Seattle
9000
Columbus
4000
New York
8000
CPUs Required
3000
5000
4000
6000
3000
21,000
a. Prepare an appropriate initial tableau
b. Obtain an initial feasible solution using the least cost method
c. Proceed using the u, v method to determine the amount that should be shipped from 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.