Question

Helpwine Module 4 irdividual part × ems 1)pdt M4 INDZ. A severe winter ice storm swept across North Carclna and Virginia, folowed by over a foot of snow and ice. These weather conditions have resulted in downed power lnes and power outages Local utility companies have requested help from some other southeastern states. The table below shows the number of crews avaiable from five companies (in Georgia, South Caroina, and Florida) and the demand for crews from seven companies (in North Carolina and Virginia). The weekly cost of the crew (in thousands of dollars) s shown in the table and is based on how far they have to travel and the living oopenses in the are Crew NC-1 NC-2 NC-3 NC4 VAİ VA-2 -WA3 GA-1 GA 2 SC-1 FL-1 FL-2 5153.2 14.3 $13.9 $135 $14.7 $10.5 $18712 512.8 $113 $106 $120 12.7 $13.2 $1561 $124 $10s $11.3 $13.1 $12.8 $145 1 $18.2 $194 $18.2 $17.9 $207 $22.7 15 NEEDED Formulate a model that will determine the number of crews that should be sent from each utility GA, 5C) to each affected area (NG, VA) that minimines total cost a) What is the total cost to meet supply the demands in the seven areas of NC and VA? b) How mary crews are sent from Fl-i to NC-4? c) How many crews are sent from FL-2 to VA-2? d) Which supplying location did not send all ther crews to the NC or VA locations?

Answer 1

Crews NC1 NC2 NC3 NC4 VA1 VA2 VA3 Available GA1 GA2 15.2 12.8 12.4 18.2 19.3 14.3 11.3 10.8 19.4 20.2 13.9 10.6 9.4 18.2 19.5 13.5 12 11.3 17.9 20.2 14.7 12.7 13.1 20.5 21.2 10 16.5 13.2 12.8 20.7 21.3 18.7 15.6 14.5 22.7 23.5 12 10 14 15 12 4 FL1 FL2 7 Crews needed9 Decision Variables Number of crews to be sent from each utility to each affected area 10 From To NC1 NC2 NC3 NC4 VA1 VA2 VA3 GA1 GA2 12 13 FL1 FL2

Obiective function Minimise the total cost 17 18 SUMPRODUCT(B11:H15,B2:H6) 19 20 SUM(B11:H11) 21 SUM(B12:H12) 22 SUM(B13:H13 23 SUM(B14:H14 24 SUM(B15:H15 25 SUM(B11:B15 26 -SUM(C11:C15) 27 SUM(D11:D15 28 SUM(E11:E15 29 SUM(F11:F15) 30 SUM(G11:G15 31 SUM(H11:H15) 32 Constraints =12 -13 -14 F15 -16 -B7

13 16 Objective function 17 18 19 Minimise the total cost 0 Constraints 13 10 1A 21 24 13 27 258 23 30 31 32 10 1

Solver Parameters Set Objective To: OMax By Changing Variable Cells: SAS18 ⓔMin Oyalue of: SBS11:SHS15 Subject to the Constraints: SAS20:SAS24 <= SCS20:SCS24 SAS25:SAS31 SCS25:SCS31 SBS11:SHS15integer SB511:SHS15 >= 0 Add Change Delete Reset All Load/Save 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

Decision Variables Number of crews to be sent from each utility to each affected area 10 From To NC1 NC2 NC3 NC4 VA1 10 VA2 VA3 GA1 GA2 SCI 0 6 6 6 0 0 0 0 Objective function Minimise the total cost 841 Constraints 10 14 15 14 15 6 29 10

a)

Total cost = $841

b)

Number of crews from FL1 to NC4 = 6

c)

Number of crews from FL2 to VA2 = 5

d)

FL2 didn't send all its crews