Mr$.$ Anderson owns a hardware store chain that just recruited three new assistant managers, Alice, Ben, and Carlie. Each of the three assistant

managers will be assigned to a regional store for training. There are four regional stores and they are located in Utica, Syracuse, Rochester, and

Buffalo. Mr$.$ Anderson indicates that each regional store can only get at most one new assistant manager.

The training costs are shown here in the table.

Part a$)$ Mr$.$ Anderson wants to minimize the total training cost. Use the network concept to create a network and its linear program for the above

problem. Make sure you define the variables used and clearly list the objective function and constraints. You do not need to solve the program.

Part b$)$ If Rochester store is closed due to the local city re$-$zoning restrictions and no longer accept trainees. How will you modify your linear

program from the previous part to include this update?