Premier Consulting has two consultants, Avery and Baker, who 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 combinations and are based on several factors, including project type and consultant's experience. The rates (dollar per hour) for each consultant-client combination are
Consultant Client A Client B Client C Client D
Avery 100 125 115 100
Baker 120 135 115 120
Campbell 155 150 140 130
Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled to work for each client in order to maximize the consulting firm's billings. What is the schedule and what is the total billing?
New information shows that Avery doesn't have the experience to be scheduled for Client B. If this assignment is not permitted, what impact does it have on total billings? What is the revised schedule?