operations research ( Hungarian method and true or false )

Question 1: (5 Points) (This question can be solved in 10 minutes easily) a) (Write Yes or No as your answer) Do we create offspring nodes by branching and continue to search from a parent node at the search tree of BnB algorithm if infeasible solution is obtained as the solution of the LP model in the parent node? b) (Write Yes or No as your answer) Do we create offspring nodes by branching and continue to search from a parent node at the search tree of BnB algorithm if there is a variable which is limited by only integer values in the MIP model but not integer valued at the solution of the LP model in the parent node? c) (Write Yes or No as your answer) We do not need to search more if there are some nodes at the search tree that branching is needed? d) (Write Yes or No at the end) Is the model that we solve in the root node an MIP model? e) (Write Yes or No as your answer) We finish the search if we find any integer feasible solution. Is it correct? Question 2: (35 points) (This question can be solved in 20 minutes easily)Suppose that we have 5 jobs (1, 2, 3, 4, 5) waiting for being performed and 5 machines (A, B, C, D, E) that can be used to perform these jobs. The assignment costs of the jobs to the machines are given in the following table. Find the minimum total cost one-to-one assignment between the jobs and the machines by the Hungarian Method. At the end, write your solution clearly: which job is assigned to which machine and what is the total cost in your solution? (Please give numbers to your tables like Table 1, Table2, ... in order to make it easier to follow your solution) 2 A B C D E 1 9 13 4 2 2 2 8 6 16 8 4 3 4 11 10 12 10 4 4 9 14 4 10 5 12 15 13 2 12