11. A single unit of model I requires 2.4 minutes of punch press time and 5 minutes of assembly time. It yields a profit of $0.80. A single unit of model II requires 3.0 minutes of punch press time and 2.5 minutes of welding time, and yields a profit of $0.70. Punch press department has 1200 minutes available per week; the welding department has 600 minutes available per week; and assembly has 1500 minutes available per week. Formulate a linear programming problem and solve it by graphical method to determine the product mix that yields maximum profit. 12. A machine shop has five machines and there are five jobs to be processed on these machines. The cost matrix for the jobs and machines is given below: Machines 1 2 3 4 5 A 4 8 12 4 6 B 6 7 6 3 5 Jobs C 6 7 8 8 10 D 9 6 7 10 8 E 4 4 6 5 5 Assign the jobs to machines using the Hungarian method so that the total cost is minimized. 13. The costs and requirements table for a transportation problem is given below. Solve this problem. Destinations I II III IV Total Supply 1 5 8 10 12 4,500 Sources 2 2 8 12 10 3,200 3 5 9 8 3 5,400 Total Requirements 5,000 2,000 4,800 1,300