(3) An automobile manufacturer makes cars and trucks in a factory that is divided up into two different shops. The first shop, which does the basic assembly, needs 5 worker-days per truck and 2 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 $500 and the profit per truck is $700.

(a) What are your variables and what do they represent?

(b) Write the objective quantity equation.

(c) Write the system of inequalities that describes the constraints.

(d) Graph the system of inequalities and find the vertices.

(e) How many of each