4-Two high speed copiers are to be located in the fifth floor of an office complex which houses four departments of the Social Security Administration. Coordinates of the centroid of each department as well as the average number of trips made per day between each department and the copiers' yet-to-be-determined location are known and given in Table below. Assume that travel originates and ends at the centroid of each department. Determine the optimal location, i.e., x, y coordinates, for the copiers. Dept. Coordinates # 1 2 3 8 4 X 10 10 12 y 2 10 6 5 Average number of daily trips to copiers 6 10 8 4

Answer correctly on excel and show workings

Maximal flow problem. Determin the Maximal flow from node 1 to 7

J 2 An electronics store wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given in the accompanying table. Develop a model to find the best location, assuming that straight-line distances can be used between the locations. Experiment with the model by testing each of the possible best solutions, included, to find the best location. Click here to view the data for the store locations and annual numbers of truckloads. Click here to view some possible best solutions. The best location is at____. (Type an ordered pair. Round each coordinate to the nearest integer as needed.)

a. A single facility is needed to meet the demands of four markets. The locations and demands of these four markets are shown below. Market Coordinate S Demand A (8,6) 10 B (4, 12) 15 C (3,2) 10 Ꭰ (9,6) 6 i. Using the data in Table 13.2, identify an optimal location for the new facility.

Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table:   PotentialLocations forSubstations AreasCovered A 1, 2, 5, 7 B 1, 3, 5 C 2, 4, 5 D 3, 4, 6 E 4, 5, 6 F 1, 5, 6, 7 G 1, 5, 7  xA +  xB +  xC +  xD +  xE +  xF +  xG     (area 1 covered)    xA +  xB +  xC +  xD +  xE +  xF +  xG   ≥, =, or less than or equal to (area 2 covered)    xA +  xB +  xC +  xD +  xE +  xF +  xG     (area 3 covered)    xA +  xB +  xC +  xD +  xE +  xF +  xG     (area 4 covered)    xA +  xB +  xC +  xD +  xE +  xF +  xG     (area 5 covered)    xA +  xB +  xC +  xD +  xE +  xF +  xG     (area 6 covered)    xA +  xB +  xC +  xD +  xE +  xF +  xG     (area 7 covered)     (a) Formulate an integer programming model that could be used to find the minimum number of…

An auto company currently maintains plants in Cincinnati and Tulsa to supply two distributioncenters in Boston and Phoenix. The production and distribution costs, distribution demands aswell as facility capacities are given in the table attached. b) Using the intuitive lowest cost method, determines which of the candidate locations, inaddition to existing locations, gives the initial solution with a lower cost? c) Using the solutions obtained in b), identify which distribution center still faces a shortage. d) Suppose the company has chosen Houston as their third plant and would like to know the optimaltransportation strategy that minimizes overall costs by solving a minimum-cost flow problem.Terry has defined decision variables, represented as xij, to denote the number of items shippedfrom plant i to distribution center j wherei= C(Cincinnati), T(Tulsa), and H(Houston)j= B(Boston) and P(Phoenix)

6 see pictures to solve