Producing an item requires 6 different tasks. Let tj denote the time (in seconds) to complete task j. We have: t1 = 30, t2 = 25, t3 = 35, t4 = 40, t5 = 15, t6 = 30. You would like to divide the tasks to 4 workers to constitute a production line.

a. Find the production capacity of the line for the following assignment: Worker 1 → Task 1, Worker 2→ Task 2, Worker 3→Tasks 3,4, Worker 4→ Tasks 5,6.

b. Find optimal assignment (to maximize the production capacity) if the task sequence should not be broken (task j should be done before task j + 1).

c. Find optimal assignment (to maximize the production capacity) if the task sequence can be broken (no precedence relationship between tasks).