Linear_Programming_Distribution_and_Network_Models_Homework_Questions.docx

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1.Problem 10-05Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to a maximum of 160 hourseach over the next four weeks. A third consultant, Campbell, has some administrative assignments already planned and isavailable for clients up to a maximum of 140 hours over the next four weeks. The company has four clients with projects inprocess. 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 theconsultant’s experience. The rates (dollars per hour) for each consultant–client combination are as follows:a.Choose the correct network representation of the problem.(i)(ii)
(iii)(iv)Model (i)b.Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should bescheduled 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 clientj.Max100x11+125x12+115x13+100x14+120x21+135x22+115x23+120x24+155x31+150x32+140x33+130x34s.t.1x11+1x12+1x13+1x141601x21+1x22+1x23+1x2416
01x31+1x32+1x33+1x341401x11+1x21+1x31=1801x12+1x22+1x32=751x13+1x23+1x33=1001x14+1x24+1x34=85xij≥ 0 for alli,jHours AssignedBillingAvery-Client A0$0Avery-Client B405000Avery-Client C10011500Avery-Client D00Baker-Client A404800Baker-Client B354725Baker-Client C00Baker-Client D8510200Campbell-Client A14021700
Campbell-Client B00Campbell-Client C00Campbell-Client D00Total Billing$57925c.New information shows that Avery doesn’t have the experience to be scheduled for client B. If this consultingassignment is not permitted, what impact does it have on total billings? What is the revised schedule?Hours AssignedBillingAvery-Client A40$4000Avery-Client B00Avery-Client C10011500Avery-Client D00Baker-Client A00Baker-Client B7510125Baker-Client C00Baker-Client D8510200Campbell-Client A14021700Campbell-Client B00Campbell-Client C00Campbell-Client D00Total Billing$57525
Problem 10-25Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD’s business involves rapiddelivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveriesanywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The followingnetwork shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations.a.Develop a linear programming model that can be used to find the minimum time required to make a delivery from location 1 tolocation 6. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

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