Set up Excel model as follows:

Note that we need any non zero values for coordinates for Shirley's new accommodation, in order to initialize the model
Set up Solver Parameters as follows:

It;s a nonlinear model, so Select a Solve Method: GRG Nonlinear


Click OK
The Weighted distance (or Load distance) between Shirley's new accommodation and Bungalow 5 is 162.62 .
Note that this answer is better than all of the given options. the closest is 206.58
Therefore, answer would be 206.58
A B с D E F | xl Location X Y Trips/Month 1 2 Bungalow 1 0 0 6 3 Bungalow 2 25 110 10 4 Bungalow 3 20 75 15 5 Bungalow 4 90 80 18 6 Bungalow 5 60 100 10 7 8 Shirley's new accomr 9 A 1 1 10 Straightline distance Load Distance =SQRT(SUMXMY2(B2:C2,$B$9:$C$9)) =E2*D2 =SQRT(SUMXMY2(B3:03,$B$9:$C$9)) =E3*D3 =SQRT(SUMXMY2(B4:04,$B$9:$C$9)) =E4*D4 =SQRT(SUMXMY2(B5:C5,$B$9:$C$9)) =E5*D5 =SQRT(SUMXMY2(B6:06,$B$9:$C$9)) !=E6*D6 11 Total load-distance = =SUM(F2:F6) 12 13
Solver Parameters Set Objective: $F$111 To: Max Min O Value of: 0 By Changing Variable Cells: $B$9:$C$9 Subject to the Constraints: < Add Change Delete Reset All Load/Save 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
А B C D G Trips/Month 6 10 15 18 Location X Y 1 2 Bungalow 1 0 0 3 Bungalow 2 25 110 4. Bungalow 3 20 75 5 Bungalow 4 90 80 6 Bungalow 5 60 100 7 8 Shirley's new accommodation: 9 A 49.5261 87.5607 10 11 E Straightline distance 100.60 33.24 32.09 41.17 16.26 F Load Distance 603.58 332.42 481.30 741.13 162.62 10 9 Total load-distance = 2,321.05 12
Solver Results Х Solver found a solution. All Constraints and optimality conditions are satisfied. Reports Answer Sensitivity Limits Keep Solver Solution O Restore Original Values Return to Solver Parameters Dialog Outline Reports OK Cancel Save Scenario...
Solver found a solution. All constraints and optimality conditions are satisfied. When the GRG engine is used, Solver has found at least a local optimal solution. When Simplex LP is used, this means Solver has found a global optimal solution.
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