CH13) Prove that the problem shown below is in NP (Computer Algorithms)

Job scheduling with penalties

Suppose there are n jobs j_1 ...... j_n to be executed one at a time. We are given execution times t_1 ...... t_n, deadlines d_1 ...... d_n (measured from the starting time of the first job executed), and penalties for missing the deadlines p_1 ...... p_n. Assume the execution times, deadlines, and penalties are all positive integers. A schedule for the job is a permutation of {1,2, ... , n}, where j_(1) is the job done first, j_(2) is the job done next, and so on. For a particular schedule, the penalty for the jth job is denoted as P_j, and is defined as p_j = p_(j) if job j_(j) completes after the deadline d_(j), otherwise P_j = 0. The total penalty for a particular schedule is: