In a project there are N tasks to be performed with the following data: N=number of task (task N last) (j=1,2,..,N) pj=duration of task j (number of periods) cj=cost of performing task j per period (payment), TL.

rj=revenue (cash) that will be collected when task j is completed,TL.

Bj=set of immediate predecessors of task j

Aj=set of immediate successors of task j

K0=amount of cash available at the start of the project fc= interest earned for cash per period (lending rate)

During the project when a task j is performed in a period a cash payment of cj TL is made and a revenue of rj TL is collected when task j is completed. Available cash in any period can be invested to bring a return of fc interest next period. Management does not want to allow cash available in any period be negative. Preemption of tasks are not allowed. For parts (b)-(e) describe only the changes that are needed to be done on the model of part (a). The models you develop must be in a form (Linear Expressions) that they could be solvable by commercial programming codes (like LINDO, GAMS, etc.) and clearly state the following: i) decision variables ii) additional parameters iii) constraints and objective function iv) assumptions (if any)

c) Consider the model of part a. Suppose for each task j we have two alternative durations as pj1 > pj2 and their respective unit time costs as cj1 < cj2. How would you modify the model?