Problem #1 (10 points total) A company manufactures three types of autosocortie pact (TYP1), mid size(TYP2), and large(TYP3). The resources required for, and the profit yielded by, each type of car are given in the following table: 2 TYP3 Steel required tons 1.5 3 5 Labor required (hours) 30 25 40 Profit yielded (S/unit) 2000 3000 4000 At present 6000 tons of steel and 60000 hours of labor are available. Determine the ILP model that will provide the number of cars produced for each car type that will maximize the companies' profit given the following two extra conditions: (a) If the difference between type 1 and type 2 autos produced are more than 100, then the difference between type 3 and type 1 autos should be at least 50 cars. (b) If the number of autos of type 3 produced is greater than 500 than the production of autos of type 1 should be less than or equal to 100