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1)Was Mark correct in what he said to get Jack to continue investigating the problem?

I would say yes, Mark provoked jack’s brain to re-innovate his ideas to accomplish the challenging project by throwing his questions. Mark believed in Jack that he would do his best for the project and he could not think others would do as well as jack does.

2) Should Mark just have given up on the idea rather that what he said to jack?

No, Mark is correct what he said to Jack. If Mark doesn’t took initiative to ask questions to Jack, nothing would have happened. Jack was surprised by Mark’s questions and at the end Jack was able to accomplish the project successfully.

3)

Should Mark have assigned this to someone else rather that giving Jack a second chance, and if so, how might Jack react?

Suppose, If Mark have assigned to his co-worker, then Jack would have missed the opportunity and he would have been discouraged. Henceforth upcoming projects would not be Jack’s best possibility.

4) What should Mark have done if jack still was not able to resolve the problem?

I think Mark would have encouraged Jack by giving some more time to solve the problem. Mark knows the complex project would be solved by Jack’s best knowledge. So he might not had give-up and given a chance to others.

5) Would it make sense for Mark to assign this problem to someone else now, after jack could not solve the problem the second time around?

I put an assumption of two cases. First, If the project has time to accommodate then, Mark would give third time chance to Jack by giving some more time to solve the problem. Second, if the project has no time to accommodate, then he had no other choice; he has to assign someone else to solve the problem as soon as possible.

6) What other options if any were now available to mark?

Mark should approach systematically for solving it will help him be a more effective in management. He should narrow down the problem by define the problem, determine the causes, generate ideas, select the best solution, take action.

Source:

Project Management A Systems Approach to Planning, Scheduling, and Controlling, (11th Edition, ISBN 978-1-118-02227)

http://www.project-management-skills.com/problem-solving-techniques.html