Five jobs need to be done on a certain machine. However, the setup time for each job

depends upon which job immediately preceded it$,$ as shown in the following table:

a$.$ Design a branch$-$and$-$bound algorithm for sequencing problems of this job by specifying how the branch, bound, and fathoming steps would be performed.

b$.$ Use this algorithm to solve this problem. that maximizes NPV using B&B$.$