SOLVE FOR B ONLY! MAKE SURE TO SHOW MODI METHOD.

$1.$ Premier Consulting's two consultants, Avery and Baker, can be scheduled to work for clients up to a maximum of $160$ hours each over the next four weeks. A third consultant, Campbell, has already planned administrative assignment already planned and is available for clients up to a maximum of $140$ hours over the next four weeks. The company has four clients with projects in process. The estimated hourly requirements for each of the clients over the four$-$week period are as follows:

Hourly rates vary for the consultant$-$client combination and are based on several factors, including project type and the consultant's experience. The rates $(\backslash (\backslash$$ $\backslash )$ per hour$)$ for each consultant$-$client combination are as follows:

a$.$ Develop a network representation of the problem.

b$.$ Solve the problem by using MODI methods using the Northwest Corner method as the initial solution. Determine the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm's billing. What is the schedule and what is the total billing?

c$.$ Formulate the problem as a linear program to maximize the consulting firm's billing