subject management Science

Transportation Case Problem Pine Computers Inc. 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 table shows the number of CPUs available at each plant, the number of CPUs required by each warehouse, and the shipping costs (dollars per unit): Warehouse Plant Los Pittsburgh Mobile Denver CPUS Available Washington 5 10 2 20 10 Angeles 9 30 10 6 9000 4000 8 Seattle Columbus New York CPUs Requirement 1 20 7 10 4 8000 3000 5000 4000 6000 3000 21000 Question 1. Write a mathematical model for the above problem. 2. Determine the amount that should be shipped from each plant to each warehouse to minimize total shipping cost. 3. The Pittsburgh warehouse just decreased its order by 1000 units, Will this lead to an increase or decrease in total shipping costs? Which plant will have an excess supply? Write a new mathematical model for this, and solve for the new optimal solution