A car manufacturing company has its manufacturing plants in Chennai and Mumbai in India. The company transports its cars from these manufacturing plants to its distribution centers located in Bangalore and Hyderabad to meet the demands. Currently, the Mumbai plant has 500 cars and the Chennai plant has 500 cars. The Hyderabad center demands 600 cars and the Bangalore center demands 400 cars. The cost of transportation between these locations depends on several factors including but not limited to toll, interstate tax, fuel cost, etc. The company estimates that the transportation cost to ship a car from Mumbai to Hyderabad is $40 and Mumbai to Bangalore is $80. The transportation cost to ship a car from Chennai to Hyderabad is $50 and Mumbai to Bangalore is $70. The company wants to meet the demand while minimizing the transportation costs. Develop a mathematical model for this problem and use logic to determine the solution.