An automobile manufacturer makes cars and trucks in a factory that divided up into two different shops. The fist shop, which does the basic assembly, needs 2 workers days per truck and 5 worker days per car. The second shop, which does the finishing touches, needs 3 worker days for both cars and trucks. The first shop has 180 worker days available per week and the second shop has 135 worker days available. The profit per car is $400 and the profit per truck is $600. How many of each type should be produced in order to maximize profit? What is the maximum profit?