Question

QUESTION 2 Use the table below to answer the following question(s). Shirley Templeton is a real estate agent for Paralol Realty. Shirley is given the responsibility to manage potential customers for 5 of the Realty's bungalows. These 5 bungalows are situated in close proximity. In order to make traveling easier, Shirley decides to move to a location closer to the 5 bungalows. The table below gives the location (X and Y coordinates) of the 5 bungalows along with the number of trips she would have to make to each bungalow. Create a nonlinear model based on the data given in the table below noting that the objective is to reduce the weighted distance between Shirley's accommodation and the 5 bungalows. Bungalow Location Y-coordinate 0 Trips/Month Data Location Bungalow 1 Bungalow 2 Bungalow 3 Bungalow 4 Bungalow 5 100 X-coordinate 0 25 120 90 60 75 80 100 10 15 18 10 According to the model, what is the distance between Shirley's new accommodation and Bungalow 4? O 54.62 O 14.53 O 44.76 98.21

Answer 1

Answer: 44.76

Excel model:

A B с D E F G Bungalow location 1 2 3 4 X Y 5 6 7 0 Data Location Bungalow -1 Bungalow -2 Bungalow - 3 Bungalow -4 Bungalow - 5 8 25 20 90 60 100 75 80 100 Trips/month Distance trip Distance/ month =(($C$2-C6) 2+($D$2-D6) 20.5 =E6*F6 10 =(($C$2-C7Y 2+($D$2-D7) 2) 0.5 =E7*F7 15 =(($C$2-C8) 2+($D$2-D8) 2) 0.5 =E8*F8 18 =(($C$2-C9)2+($D$2-D9) 2) 0.5 =E9*F9 10 =(($C$2-C10) 2+($D$2-D10) 2) 0.5 =E10*F10 Total distance =SUM(G6:G10) 9 10 11

Solver models:

Set Objective: $G$11 To: Max Min O Value of: 0 .... By Changing Variable Cells: $C$2:$D$2 X 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

Solution:

Bungalow location	45.55	85.24
Data
Location	X	Y	Trips/ month	Distance/ trip	Distance/ month
Bungalow -1	0	0	6	96.65	579.87
Bungalow -2	25	100	10	25.30	252.99
Bungalow -3	20	75	15	27.52	412.84
Bungalow -4	90	80	18	44.76	805.69
Bungalow -5	60	100	10	20.66	206.58
				Total distance	2257.98