# Develop a network representation of the problem.

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  (4) weeks. A third consultant Campbell has some adminstrative assignments already planned and is availble for clieents up to a maximum of 140 hours over the next four (4) weeks. The company has four (4) clients with projects in process. The estimated hourly requirments for each of the clients over the four-week period as follows:

CLIENT                         HOURS

A                                      180

B                                      75

C                                      100

D                                      85

Hourly rates vary form the consultant-client combinations and are based on several factors, including project type and consultants” experince. The rates( dollars per hour) for each consultants-client combination are as follows:                                                                   CLIENT

CONSULTANTS                            A              B                    C                   D

AVERY                                        100             125               115              100

BAKER                                         120             135             115               120

CAMPBELL                                  155             150            140               130

a) Develop a network representation of the problem.

b) formulate the problem as linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing?

c)New information shows that Avery doesn’t have the experince to be scheduled for client B. If this consultingnassignment is not premitted, what impact does it have on total billings? What is the revised scheduled?

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