(Solved): Old McDonald is trying to decide how best to assign his farmhands Elanor, Dash, Delilah and Jemima t ...

Old McDonald is trying to decide how best to assign his farmhands Elanor, Dash, Delilah and Jemima to manage three jobs that need doing on the farm. The time required to complete each of the jobs (in hours) is shown in the table below if Elanor, Dash, Delilah or Jemima manage the job.

Old McDonald decides to avoid any conflict that only one farmhand will manage each job.

There will be no cost in terms of time incurred if one of the farmhands is idle.

 (a) Determine the assignment which minimizes the total time using the Hungarian method. List this minimum time. Which farmhand is idle?

(b) Suppose the Old McDonald changes his mind and decides that Dash being idle is costing the farm 11 hours. Determine how this affects the assignment of the farmhands.

Which farmhand should be allocated to manage each job and what is the minimum total time.