Question: Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to…

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Jun 13, 2022

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Question: Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to…

by | Jun 13, 2022 | Questions & Answers


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
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:

A B C 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
for each client to maximize the consulting firm’s billings. What is
the schedule and what is the total billing?

Let xij = number of hours from consultant i assigned to
client j.

Max 100x11 + 125x12 + 115x13 + 100x14 + 120x21 + 135x22 + 115x23
+ 120x24 + 155x31 + 150x32 + 140x33 + 130x34
s.t. 1x11 + 1x12 + 1x13 + 1x14 160
1x21 + 1x22 + 1x23 + 1x24 160
1x31 + 1x32 + 1x33 + 1x34 140
1x11 + 1x21 + 1x31 = 180
1x12 + 1x22 + 1x32 = 75
1x13 + 1x23 + 1x33 = 100
1x14 + 1x24 + 1x34 = 85
xij ≥ 0 for all i,
j

Hours Assigned Billing
Avery-Client A 0 $0
Avery-Client B 40 5000
Avery-Client C 100 11500
Avery-Client D 0 0
Baker-Client A 40 4800
Baker-Client B 35 4725
Baker-Client C 0 0
Baker-Client D 85 10200
Campbell-Client A 140 21700
Campbell-Client B 0 0
Campbell-Client C 0 0
Campbell-Client D 0 0
Total Billing $ 57925

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 cannot calculate these answers. Other
posts on Chegg have had incorrect answers. Please start new work to
solve this question.

Hours Assigned Billing
Avery-Client A $
Avery-Client B
Avery-Client C
Avery-Client D
Baker-Client A
Baker-Client B
Baker-Client C
Baker-Client D
Campbell-Client A
Campbell-Client B
Campbell-Client C
Campbell-Client D
Total Billing $

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