Four jobs must be processed on a single machine. The time required to perform each

job, the due date, and the penalty

$($

in dollars

$)$

$$per day the job is late are given in below

table:

a

$.$

$$Design a branch

$-$

and

$-$

bound algorithm for this single machine problem specifying

how the branch, bound, and fathoming steps would be performed.

b

$.$

$$Use this algorithm to solve this problem.