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1) Machine Shop Layout Design (30 Points) The figure below shows the layout of a machine shop with four existing workstations indicated by the squares 1,2,3 and 4. Shop owner wishes to add four new workstations (I, II, III and IV) to the areas indicated by the circles a, b, c and d. The objective is to assign the new centers to the proposed locations to minimize the total materials handling traffic between the existing centers and the proposed ones. 70 60 50 3 40 - 2 30 - 20 4 10 - d 0 10 20 30 40 50 60 70 80 The table below shows the daily frequency of trips between the new workstations and the old ones. New station I II III IV 10 2 4 3 7 1 9 5 0 8 6 2 11 4 0 7 1 2 3 4. Existing station Materials handling equipment travels along the rectangular aisles intersecting at the locations of the workstations. For example, the one-way travel distance (in meters) between workstation 1 and location bis 30 + 20 = 50 m. Using the information given above, perform the following: a) [20pt] Formulate a linear programming problem to assign the four new workstations to the locations (a)-(d) such that the total materials handling traffic is minimum. Report the resulting transportation tableau. Hint: Check Lecture 10-1, Slide 7 for an example transportation tableau. An empty version should look like below: (a) (b) (c) (d) Supply I II III IV Demand Hint: This is an assignment problem. Hint: You need to calculate the cost of assigning stations I-IV to locations (a)-(d) to fill out the transportation tableau. The easiest way to do it is as follows: - Assume that the 4x4 table given to you above is called K, measuring the frequency of visits from the existing stations (1-4) to the new ones (I-IV). Calculate another 4x4 table L measuring the distances from existing stations 1-4 to the locations (a)-(d) using the figure. - Calculate the 4x4 cost matrix C = KTL defining the costs that you need for the transportation tableau. b) [10pt] Solve the linear programming problem defined in part a) using Excel's solver. Report the total cost and the locations of the new workstations at the optimum