We are given n tasks to be completed on a single machine. Task i requires pi units of

processing time on the machine; task i also has $$weight$$ wi$,$ profit Bi$,$ and a deadline di$.$

You may assume that wi and pi are positive integers. Completing task i at time T yields a

net benefit of Bi $$ wiT $.($Think of Bi as the benefit of completing task i$,$ but task i incurs

a waiting cost of wi for each unit of time until it is fully completed.$)$ Moreover, if a task i

completes after its deadline di$,$ then an additional cost of Ri in incurred. You can complete

the tasks in any order and your goal is to sequence the tasks to maximize the total benefit

accrued by completing all of them. Formulate this problem as an integer programming

problem.