You are the plant supervisor and are responsible for scheduling workers to jobs on hand. After estimating the cost of assigning each of five available workers in your plant to five projects that must be completed immediately, you solve the problem using the Hungarian method. The following solution is reached and you post these job assignments:
Jones to project A
Smith to project B
Thomas to project C
Gibbs to project D
Heldman to project E
The optimal cost was found to be $492 for these assignments.
The plant general manager inspects your original cost estimates and informs you that increased employee benefits mean that each of the 25 numbers in your cost table is too low by $5. He suggests that you immediately rework the problem and post the new assignments.
Is this necessary? Why? What will the new optimal cost be?