Premier Consultings two consultants, Avery and Baker, can be scheduled to work for clients up to a

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 some administrative assignments 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

Client Hours

A .......180

B ........ 75

C ........100

D ......... 85

Hourly rates vary for the consultant–client combination and are based on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant–client combination are

a. Develop a network representation of the problem.
b. Formulate the problem as a 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 experience to be scheduled for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revisedschedule?

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Client Consultant Avery Baker Campbell 100 120 155 9 125 135 150 115 115 140 100 120 130