[SOLVED] Network representation..

[SOLVED] Network representation..

network representation 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:

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:

1. Choose the correct network representation of the problem.
 (i) (ii) (iii) (iv)
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?Let xij = number of hours from consultant i assigned to client j.
 Max fill in the blank 2x11 + fill in the blank 3x12 + fill in the blank 4x13 + fill in the blank 5x14 + fill in the blank 6x21 + fill in the blank 7x22 + fill in the blank 8x23 + fill in the blank 9x24 + fill in the blank 10x31 + fill in the blank 11x32 + fill in the blank 12x33 + fill in the blank 13x34 s.t. fill in the blank 14x11 + fill in the blank 15x12 + fill in the blank 16x13 + fill in the blank 17x14 ≤ fill in the blank 18 fill in the blank 19x21 + fill in the blank 20x22 + fill in the blank 21x23 + fill in the blank 22x24 ≤ fill in the blank 23 fill in the blank 24x31 + fill in the blank 25x32 + fill in the blank 26x33 + fill in the blank 27x34 ≤ fill in the blank 28 fill in the blank 29x11 + fill in the blank 30x21 + fill in the blank 31x31 = fill in the blank 32 fill in the blank 33x12 + fill in the blank 34x22 + fill in the blank 35x32 = fill in the blank 36 fill in the blank 37x13 + fill in the blank 38x23 + fill in the blank 39x33 = fill in the blank 40 fill in the blank 41x14 + fill in the blank 42x24 + fill in the blank 43x34 = fill in the blank 44 xij ≥ 0 for all i, j
 Hours Assigned Billing Avery-Client A fill in the blank 45 \$fill in the blank 46 Avery-Client B fill in the blank 47 fill in the blank 48 Avery-Client C fill in the blank 49 fill in the blank 50 Avery-Client D fill in the blank 51 fill in the blank 52 Baker-Client A fill in the blank 53 fill in the blank 54 Baker-Client B fill in the blank 55 fill in the blank 56 Baker-Client C fill in the blank 57 fill in the blank 58 Baker-Client D fill in the blank 59 fill in the blank 60 Campbell-Client A fill in the blank 61 fill in the blank 62 Campbell-Client B fill in the blank 63 fill in the blank 64 Campbell-Client C fill in the blank 65 fill in the blank 66 Campbell-Client D fill in the blank 67 fill in the blank 68 Total Billing \$  fill in the blank 69
3. 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?
 Hours Assigned Billing Avery-Client A fill in the blank 70 \$fill in the blank 71 Avery-Client B fill in the blank 72 fill in the blank 73 Avery-Client C fill in the blank 74 fill in the blank 75 Avery-Client D fill in the blank 76 fill in the blank 77 Baker-Client A fill in the blank 78 fill in the blank 79 Baker-Client B fill in the blank 80 fill in the blank 81 Baker-Client C fill in the blank 82 fill in the blank 83 Baker-Client D fill in the blank 84 fill in the blank 85 Campbell-Client A fill in the blank 86 fill in the blank 87 Campbell-Client B fill in the blank 88 fill in the blank 89 Campbell-Client C fill in the blank 90 fill in the blank 91 Campbell-Client D fill in the blank 92 fill in the blank 93 Total Billing \$fill in the blank 94

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