Question

c. How much should both red and blue GloFish while man duced at the Texas farm? Premier Consulting's two consultants, Avery and Baker, can be sch clients up to a maximum of 160 hours each over the next four week tant, Campbell, has some administrative assignments already planned clients up to a maximum of 140 hours over the next four weeks. The clients with projects in process. The estimated hourly requirements for eac over the four-week period are as follows: he scheduled to work for ur weeks. A third consul- anned and is available for The company has four ements for each of the clients Client Hours 180 75 100 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 Avery Baker Campbell 120 125 135 150 115 115 140 130 solution providing the a. Develop a network representation of the problem. b. Formulate the problem as a linear program, with the optimal solution hours each consultant should be scheduled for each client to maximize firm's billings. What is the schedule and what is the total billing? c. New information shows that Avery doesn't have the experience to be client B. If this consulting assignment is not permitted, what impact total billings? What is the revised schedule? 6. Klein Chemicals, Inc., produses in mize the consulting to be scheduled for impact does it have on lan

Answer 1

Answer:

a. Develop a network representation of the problem:

180 100 160 Avery 115 \100 120 135 Baker 160 115 Van 100 135/ 150 140 Campbell 140 130

b.

LPP Max noor11 = 123x12 + 1513 : 1eos 14 + 12021 + 1352 + 123 + 120x24 - 15331 : 150x32 + 140x3 + 13034 11 +[ 12 +[ 13 +14 21 + 122 | 23 | 24 st. + 32 + x33 + x 34 11 | x31 + x 31 + | 21 | + x22 12 12 + 32 در 13 | + x33 + | 23 x 14 |+ | 24 | + x 34 xij >= 0 for all i,j

|_ A B C D E F G H Client A B C D 125 2 Consultant 3 Avery 100 Baker 120 5 Campbell 155 135 150 115 115 140 100 120 130 D =SUM(B10:E10) <= 160 =SUM(B11:E11) <= 160 =SUM(B12:E12) <= 140 Client 9 Consultant A B C 10 Avery 11 Baker 12 Campbell 13 =SUM(B10:B12) I=SUM(C10:C12) I=SUM(D10:012) 14 75 100 16 17 Total Rate =SUMPRODUCT(B3:E5,B10:E12) =SUM(E10:E12) 180

Solver Parameters Set Objective: $D$17 To: O Max O Min O Value Of: By Changing Variable Cells: $B$10:$E$12 Subject to the Constraints: $B$13:$E$13 = $B$15:$E$15 $F$10:$F$12 <= $H$10:$H$12 Add Change Delete Reset All Load/Save v Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

A B E F. G H 1 2 3 4 5 Consultant Avery Baker Campbell А. 100 120 C D Client LBC 125 115 135 115 150 140 100 120 130 155 Client A 0 / <= L 8 9 Consultant 10 Avery 11 Baker 12 Campbell 13 в 40 35 0 с 100 0 0 100 D 0 85 O 85 140 160 40 160 160 140 140 140 180 15 180 75 1 100 85 16 17 Total Rate 57925

Hours Assigned Billing O 5000 11500 0 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 40 100 0 40 35 0 4800 4725 85 140 10200 21700 O 0 0 O 57925

c.

If Campbell cannot work any more x31, x32, x33, 234 = 0 Avery and Baker can handle up to two clients at a time. HEnce, aij, a binary variable, represent the decision to which clients are the consultants handling, with aij = 1 if the consultant i is handling client j and aij = 0 if consultant i is not handling the clinetj. Added constraint: all + al2 + al3+ al4 = 2 a21 + a22 + a23+ a24 = 2 Avery and Baker can work with all clients, have now double the amount of previous time to work, hence, the supply constraints change to: Supply constraints: xll* all + x12* al2 +xl3* al3 +x14* al4 <= 320 ( Avery) X21* a21 +*22* a22 +x23* a23 +x24* a24 <= 320 ( Baker) Demand Constraints: xll* all + x21* a21 = 180 (Client a) x12* al2 + x22* a22 = 75 (Client b) x13* al3+x23* a23 = 100 (Client c) x14* al4 + x24* a24 = 85 (Client d)

ДА E G H Client ATBT 2 Consultant Avery 4 Baker 3 Avery 100 120 100 - 125 115 5 IB = =SUM(B8:E8) =SUM(B9:59) 10 Client 7 Consultant Avery 9 Baker Avery Baker 12 13 Avery =B8*B10 =C8*C10 =D8*D10 14 Baker =B9*B11 =C9*C11 =D9*D11 =SUM(B13:B14) =SUM(C13:C14) =SUM(D13:014) 11 =E8*E10 =E9*E11 =SUM(E13:E14) =SUM(B13:E13) <= =160*2 =SUM(B14:E14) <==160*2 180 75 100 85 Total Rate =SUMPRODUCT(B3:E4,B13:E14)

X Solver Parameters Set Objective: $D$19 To: O Max O Min O Value of: By Changing Variable Cells: $B$8:$E$9,$B$10:$E$11 Add Subject to the Constraints: $B$8:$E$9 = binary $F$13:$F$14 <= $H$ 13:$H$14 $B$15:$E$15 = $B$17:$E$17 $F$8:$F$9 = $H$8:$H$9 Change Delete Reset All Load/Save v Make Unconstrained variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

2 3 4 Consultant Avery Baker A 100 120 DE F Client D 115 100 115 120 125 135 Client A 0 0 7 8 9 10 11 12 Consultant Avery Baker Avery Baker 180 7620 100 Avery Baker 0 180 180 175 265 320 320 O <= 100 180 100 | Total Rate 52675

Total billings have reduced. An Revised schedule: Client BC 75 100 0 0 Avery Baker 180 85 Hours Assigned Billing 9375 11500 100 0 Avery-Client A Avery-Client B Avery-Client C Avery-Client D Baker-Client A Baker-Client B Baker-Client C Baker-Client D Total Billing 180 21600 O 10200 52675