Formula Sheet 1.5 30 3 25 5 40 4000 Problem #1 (10 points total) A company manufactures three types of autos profit 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 tables TYP1 TYP2 TYP3 Steel required tons Labor required (hours) Profit yielded (S/unit) 2000 3000 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 produoed 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 Problem #4 (10 points total) The figure below shows the available route between sup pliers and distributors. The suppliers are represented by nodes 1, 2, and 3 whose supply amounts are (100), [200), and (50) units of product, respectively. The distributors are resented by no 4, 5, and 6 whose demand amounts are (-150), (-80), and (-120) units of product, respectively. The routes allow transshipping between the suppliers. Arcs (1.4), (3,4), and (4,6) are truck routes. These rotates have minimum and maximum capacities. For example, the capacity of route (1.4) is between 50 and 80 units of product only as shown beneath the are in the figure. All other routes use trainloads, whose maximum capacity is practically unlimited. The transportation costs per unit of product are indicated on the respective arcs. Write a linear program that will minimize transportation cost while meeting supply/demand and capacity constraints. 1100 52 1-1501 $1 (341, 801) 51 ISO (10.120) $4 53 61-1201 $4 -3 SS (100, 120) 2001 2 I- Formula Sheet 1.5 30 3 25 5 40 4000 Problem #1 (10 points total) A company manufactures three types of autos profit 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 tables TYP1 TYP2 TYP3 Steel required tons Labor required (hours) Profit yielded (S/unit) 2000 3000 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 produoed 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 Problem #4 (10 points total) The figure below shows the available route between sup pliers and distributors. The suppliers are represented by nodes 1, 2, and 3 whose supply amounts are (100), [200), and (50) units of product, respectively. The distributors are resented by no 4, 5, and 6 whose demand amounts are (-150), (-80), and (-120) units of product, respectively. The routes allow transshipping between the suppliers. Arcs (1.4), (3,4), and (4,6) are truck routes. These rotates have minimum and maximum capacities. For example, the capacity of route (1.4) is between 50 and 80 units of product only as shown beneath the are in the figure. All other routes use trainloads, whose maximum capacity is practically unlimited. The transportation costs per unit of product are indicated on the respective arcs. Write a linear program that will minimize transportation cost while meeting supply/demand and capacity constraints. 1100 52 1-1501 $1 (341, 801) 51 ISO (10.120) $4 53 61-1201 $4 -3 SS (100, 120) 2001 2