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

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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
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
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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