Megamotor produces Type 1 car and Type 2 car. Each car must go to the assembly station first and then it must be painted in a painting station. If the capacity of the assembly station is totally allocated to assembling Type 1 car, then 2,400 cars per month can be produced; if the capacity of assembly station is totally allocated to assembling Type 2 car, then 2,100 cars per month can be produced. If the capacity of the painting station is totally allocated to Type 1 cars, then 650 cars per month can be painted; if the capacity of the painting station is totally allocated to painting Type 2 cars, then 390 cars per month can served in this station Selling each Type 1 car results in $300 of profit, while selling of each Type 2 car results in $500 of profit. 

Formulate a linear programming model that will maximize Megamotor's profit.

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