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 as follows.

Client	Hours
A1	180
B2	75
C3	100
D4	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
Avery1	100	125	115	100
Baker2	120	135	115	120
Campbell3	155	150	140	130

(A) 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.

(i) Let x_ij = number of hours from consultant i assigned to client j, using the indices from the tables. For example, x₃₄ is the number of hours Campbell spends with Client D.

Max _______

s.t.

Assignments for Avery ____ (PLEASE PROVIDE ANSWER HERE)

Assignments for Baker ____ (PLEASE PROVIDE ANSWER HERE)

Assignments for Campbell ____ (PLEASE PROVIDE ANSWER HERE)

Assignments to Client A ____ (PLEASE PROVIDE ANSWER HERE)

Assignments to Client B ____ (PLEASE PROVIDE ANSWER HERE)

Assignments to Client C _____ (PLEASE PROVIDE ANSWER HERE)

Assignments to Client D _____ (PLEASE PROVIDE ANSWER HERE)

x_ij 0 for all i, j.

(ii) What is the schedule?

(x₁₁, x₁₂, , x₃₃, x₃₄) = ______ (PLEASE PROVIDE ANSWER HERE)

(iii) What is the total billing? (Express your answer in dollars. Round you answer to the nearest whole number.)

$ _______ (PLEASE PROVIDE ANSWER HERE)

(B) 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 revised schedule?

(i) revised schedule

(x₁₁, x₁₂, , x₃₃, x₃₄) = ______ (PLEASE PROVIDE ANSWER HERE)

(ii) impact on billing

Due to the change total revenue will ---Select--- rise OR fall . (PLEASE PROVIDE ANSWER HERE)

Please provide the answers clearly for each section, thank you.