An automobile manufacturer has contracted to export 400 cars of model A and 500 cars of model B overseas. The model A car occupies a volume of 12 cubic meters, and the model B car occupies a volume of 15 cubic meters. Three ships for transporting the automobiles are available. They arrive at the port of destination at the beginning of January, the middle of February, and the end of March respectively. The first ship only transports model A cars at Rs. 9000 per automobile. The second and third ships transport both types at a cost of Rs. 700 and Rs. 800 per cubic meter respectively. The first ship can only accommodate 200 cars, and the second and third ships have available volumes of 4500 and 6000 cubic meters. If the manufacturer has contracted to deliver at least 250 and 200 cars of model A and B by the middle of February and the remainder by the end of March, what is the shipping pattern that minimizes the total cost? Formulate the LP problem