General Ford produces cars in Los Angeles and Detroit and has awarehouse in Atlanta. The company supplies cars to customers inHouston and Tampa. The costs of shipping a car between variouspoints are listed in the file P05_54.xlsx, where a blank means thata shipment is not allowed. Los Angeles can produce up to 1600 cars,and Detroit can produce up to 3200 cars. Houston must receive 1800cars, and Tampa must receive 2900 cars. a. Determine how tominimize the cost of meeting demands in Houston and Tampa. b.Modify the answer to part a if no shipments through Atlanta areallowed.
| unit shipping cost | | | | | | | | |
| | to | | | | | | | |
| | LA | Detroit | Atlanta | Houston | Tampa | | | |
| from | LA | | $97 | $95 | $125 | $156 | | | |
| Detroit | $94 | | $103 | $110 | $148 | | | |
| Atlanta | $87 | $100 | | $95 | $56 | | | |
| Houston | $129 | $103 | $88 | | $100 | | | |
| Tampa | $147 | $145 | $60 | $103 | | | | |
| | | | | | | | | |
| | | | | | | | | |
| network formulation | | | | flow balance contraints | | |
| origin | destination | cost | flow | | location | index | net flow in/out | Required |
| 1 | 2 | $97 | | | LA | 1 | | <= | |
| 1 | 3 | $95 | | | Detroit | 2 | | <= | |
| 1 | 4 | $125 | | | Atlanta | 3 | | = | |
| 1 | 5 | $156 | | | Houston | 4 | | = | |
| 2 | 1 | $94 | | | Tampa | 5 | | = | |
| 2 | 3 | $103 | | | | | | | |
| 2 | 4 | $110 | | | | | | | |
| 2 | 5 | $148 | | | | | | | |
| 3 | 1 | $87 | | | | | | | |
| 3 | 2 | $100 | | | | | | | |
| 3 | 4 | $95 | | | | | | | |
| 3 | 5 | $56 | | | | | | | |
| 4 | 1 | $129 | | | | | | | |
| 4 | 2 | $103 | | | | | | | |
| 4 | 3 | $88 | | | | | | | |
| 4 | 5 | $100 | | | | | | | |
| 5 | 1 | $147 | | | | | | | |
| 5 | 2 | $145 | | | | | | | |
| 5 | 3 | $60 | | | | | | | |
| 5 | 4 | $103 | | | | | | | |
total cost
