1. A car company is capable of manufacturing 4 types of Cars: type 1, type 2,type3, and type 4. The resources required for, and the profits yielded by, each type of them are shown in the following table. Currently, 5,000 tons of steel, 1,000 tons of iron and 50,000 hours of labor are available. The manufac- ture of each type of car requires that the company have the appropriate type of machinery available. The machinery needed to manufacture each type of car must be rented at the following rates: Type 1 machinery, $200; Type 2 machinery, $120; Type 3 machinery, $150; and Type 4 machinery, $100. For production of a type of car to be economically feasible, at least 2,000 cars of that type must be produced. Also, the company must rent at least two type of machinery. In addition, they cannot rent type 1 and type 3 machinery in the same time(which means at most one of them can be rented).Formulate an IP to maximize the company profit. type 1 2 tons 2 tons resource Steel required Iron required type 2 type 3 1 tons 1 tons Labor required 30 hours Profit yielded 3000 2 tons 20 hours 4000 2 tons 40 hours type 4 3 tons 1 tons 20 hours 3000 5000 (a)Write the decision variables and give the meaning of each decision variable (4 points) (b) Write the objective function (2 points) (c) Write the whole LP model and state the meaning of each constraint (14 points)