Quality Consulting has two consultants, Alfred and Barbara that can be scheduled to work for clients up to a maximum of 170 hours each over the next four weeks. A third consultant, Charlie, has some administrative assignments already planned and is available for clients up to a maximum of 150 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 as follows:

Client
Consultant
A
B
C
D
Alfred
100
125
115
100
Barbara
120
135
115
120
Charlie
155
150
140
130

1) Develop a network representation of the problem. You may reference the Network Diagram Template .

2) 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?