Question

TN Communications provides cellular telephone services. The company is planning to expand into the Cincinnati area and is trying to determine the best location for its transmission tower. The tower transmits over a radius of 10 miles. The locations that must be reached by this tower are shown in the following figure...

TN Communications provides cellular telephone services. The company is planning to expand into the Cincinnati area and is trying to determine the best location for its transmission tower. The tower transmits over a radius of 10 miles. The locations that must be reached by this tower are shown in the following figure, Hide Park Florence 18 12 Covington 12 16 Hyde Park 16 18 Evendale 12 22 TN Communications would like to find the tower location that reaches each of these cities and minimizes the sum of the distances to all locations from the new tower. Round your answers to two decimal digit. (a) Formulate and solve a model that minimizes the total distance between the transmission tower location and all the city locations. 12 18 Tower location Max Distance 4 miles (b) Formulate and solve a model that minimizes the maximum distance from the transmission tower location to the city locations. 12 18 Tower location Max Distance 6 miles

Answer 1

a)

D E Solver Parameters A B C х у e optimal value 14.76921 17.38459 Set Objective: $D$10 y To: O Max Min O value of: 18 12 16 Distance 12 6.279477 16 3.096062 18 1.376074 22 5.382427 By Changing Variable Cells: $B$2:$C$2 Subject to the Constraints: Add O Sum 16.13404 Change Nm Delete Reset All Load/Save Make Unconstrained variables Non-Negative 00 Select a Solving Method: GRG Nonlinear Options O-NM 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

optimal location for minimum distance

x = 14.7692

y = 17.3846

Max distance = 16.1340

Formulas

в с р 2 optimal value 14.7692071402759 17.384589857107 Distance =SQRT(($B$2-B5)^2 + ($C$2-C5)^2) =SQRT($B$2-B6)^2 + ($C$2-C6)^2) =SQRT($B$2-B7)^2 + ($C$2-C7)^2) =SQRT($B$2-B8)^2 + ($C$2-C8)^2) 18 Sum =SUM(D4:08)

Data -> solver