A disaster relief center needs to process 20 tasks in sequence. Each task has a known processing time (in hours), a due date (derived from the urgency of each task) and a penalty (which is an importance factor associated with each task.)

Task	1	2	3	4	5	6	7	8	9	10
Time	14	10	9	7	14	12	9	7	8	13
Due	118	45	97	169	95	99	81	194	139	61
Penalty	10	10	8	9	8	10	7	9	6	10
Task	11	12	13	14	15	16	17	18	19	20
Time	12	7	11	12	9	14	11	8	8	10
Due	34	124	161	187	64	75	152	184	153	117
Penalty	7	6	6	9	7	8	5	9	10	7

In this situation, the objective is to minimize the weighted tardiness. In other words, if a task is completed by its due date, then no penalty is incurred. If a task completes after its due date, the weighted tardiness is the penalty factor multiplied by the tardiness. For instance, if the tasks are processed in the order in which they are numbered, then task 1 would be completed at time 14, task 2 would be completed at time 24 (i.e., 14 + 10). Both tasks would be on time, because their due dates are 118 and 45, respectively. If all tasks are processed using their task number as the order, then the first late task would be task 10, which we be completed at time 103 (i.e., the sum of the times for tasks 1 to 10). Task 10s tardiness would be 103-61 = 42 and its weighted penalty would be 420 (i.e., 42*10).

a. Suppose the measure of scheduling effectiveness is the sum of the penalties for the late tasksthat is, the total weighted tardiness. Build an evolutionary solver model for this problem. Initialize the optimization with the order given by the task number. What is the best (smallest) possible value of the total weighted tardiness?

b. Suppose instead that the measure of scheduling effectiveness is the worst of the penalties for all late tasksthat is, the maximum weighted tardiness. What is the best (smallest) possible value of the maximum weighted tardiness?