Mcpies International Limited manufactures expensive cars in Japan and then exports some cars to sell in Australia. John Automotive in Australia is currently handling the dealership across Australia for the incoming cars from Mcpies International Limited. The exported cars are shipped from Tokyo to Brisbane, Sydney, and Melbourne ports. The cars are transported by rail or truck to distributors located in Perth, Canberra, Adelaide, Alice Springs and Darwin from these ports.

Currently, 60 cars are available at the port in Brisbane, 80 are available in Sydney and 100 in Melbourne. The numbers of cars needed by the distributors in Perth, Canberra, Adelaide, Alice Springs and Darwin are 70, 70, 80, 40, and 40, respectively. John Automotive needs to determine the least costly way of transporting cars from the ports in Sydney, Melbourne and Brisbane to the cities where they are required. Notably, costs mentioned over the arrows are costs per car transported.

Now,
a) Formulate a linear programming model (showing the decision variables, objective function and constraints) that can be used to determine the number of cars to be shipped from each port to each demand city.

b) Solve the LP model by Excel Solver and determine the minimum transportation cost that John Automotive incurs?

c) How many cars are shipped from each port to each demand city?

 

3 PERTH +70 $1200 $700 $1400 $1000 $900 8 DARWIN +40 $800 $1100 $1900 $800 $1300 2 ADELAIDE +80 7 ALICE SPRINGS +40 $1800 $1000 $800 $400 $1500 $1300 $1500 $800 $900 $800 5 CANBERRA +70 $600 $450 6 BRISBANE -60 4 MELBOURNE -100 $900 $250 1 SYDNEY -80