Dear Expert, please create the visual chart for Part A of this question: Ms$.$ Smith is the CEO of an Artificial Intelligence company. She just recruited three new college graduates, Jeff, Steve, and Linda. Each of the three graduates will be assigned to a regional office for training. There are four regional offices and they are located in Austin, Pittsburgh, Nashville, and Springdale. Ms$.$ Smith indicates that each regional office can only accept at most one college graduate for training.

The training costs are shown here in the table.

Trainees$/$Offices Austin Pittsburgh Nashville Springdale

Jeff $$510$ $$455$ $$522$ $$400$

Steve $$412$ $$510$ $$420$ $$400$

Linda $$520$ $$480$ $$507$ $$405$

Part a$)$ Ms$.$ Smith 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 the Pittsburgh store is closed due to the local city re$-$zoning restrictions and no longer accepts college graduate trainees. How will you modify your linear program from the previous part to include this update?