(35 points) Six work centers (WCs) will be located in a workshop. Table 1 shows the number of parts transferred between each pair of WCs per month and Table 2 is to be used for assessing the relationship among WCs. For instance, if more than 1,000 parts are exchanged between two WCs per month, to place them next to each other is Absolutely (A) important and for relevant computations, its value is 4. WC WC WC WC4 WCS WOR Wa 850 200 No of Products wa 650 0180 wa moving per month Cassification/ Greater than 3000 Fremd000 to 800 VUI 4 WCI wa 450 200 250 550 180 1100 2 From 4390 was Table 1 Table 2 a. (10 points) Set up the relationship chart and draw the relationship diagram. Consulting Table 2, the V-) between WC2 and WC4 is (only integers). b. (10 points) Assuming equal areas for each WC, someone came up with the layout provided in Figure 1. Assume that the cost of moving any part per block (horizontally or vertically) is 1. Consider rectilinear distances (e.g. between WC3 and WC1, it is 1 block between WC3 and WC2, it is 2 blocks; between WC3 and WC4, it is 3 blocks). Observe that two WCs are adjacent if they share an edge (such as WC2 and WC6), sharing only a corner does not imply adjacency (e.g., WC2 and WCS are not adjacent). WC2 WC6 WC4 WCS Figure 1 WC3 WC1 Calculate the relative adjacency score of this layout. Then, calculate the total monthly cost of moving parts according to this layout. The monthly total cost of moving parts is (only integers). c. (5 points) Would swapping WC2 and WC6 give an improved layout compared to the one in Figure 1? Answer this question considering the monthly transportation cost as the criterion The absolute value of difference in cost after swapping is (only integers). d. (10 points) Each WC is identical in size with a horizontal length of 10 m and a vertical length of 8 m. Consider the mixed-integer LP formulation that would place these WCs in a workshop that has a horizontal length of 60 m and a vertical length of 20 m minimizing the total monthly cost of moving parts. Assume that the distances are rectilinear and the moving cost is 1 for unit per meter. Write all the constraints. that relate WC1. to WC2. Introduce any necessary variables and explain what these constraints do. Provide the term in the objective function that is related to both WC1 and WC2. DO NOT use a generic formulation.