only a and c

for a ( draw graph as with Figure 10.10 )

for c ( use solver use Solver for rectilinear solution)

10.9 The city council of Fayetteville has decided to locate an emergency response unit within the city. This unit is responsible for four housing sectors (A) and three major street intersections (P) as shown in the figure below. Assume that the weights are uni- formly distributed over the housing sectors. a. Determine the minisum location based on the weights given in the table below, as- suming no restrictions apply to the location of the emergency response unit. b. Determine the minisum location assuming the new facility cannot be located within a housing sector. c. Determine the minimax location by measuring distances to the centroids of areas and using the weights given in the table below. d. Determine the minimax location based on equal weights and measuring distance to the farthest point in an area. Housing Sector Weight Intersection Weight A P 30 A2 15 Az 20 Ps 30 10 P2 15 5 15 Az Az P2 10 . y-axis a 2 . 5 A ". 0 0 5 10 15 X-axis 1.0 0.9 - 0.8 0.7 - - 0.6 half-weight line Weight consumption (Moving from Left to Right) Along the x-Axis 0.5 0.4 0.3 0.2 0.1 -- optimum value of x 0 0 3 4 6 7 8 9 10 2 5 x-Axis Figure 10.10 Solving for the optimum x-coordinate for the new facility in Example 10.4