Question 5 [30 points). A machine shop is facing a problem of locating four machines along an aisle. The machine dimensions are known in Table 1 below. The material handling trips between machines are available in Table 2 below. The cost of the trips among the machines are available in Table 3 below. A clearance of l' is required between any two machines. Based on the above information, please place the machines along the aisle. To unify the results, assume the machine shop wants to sequence the order of the machines from a small index to a large index if multiple layout options are possible (for example, if the set of machines 1 and 4 is selected in the first step, we would order the machines as 14. Note that this rule only applies to the first step of the algorithm). Table 1. Machine Dimensions (in feetx feet) Machine 1 2 3 4 Dimensions 6x6 5x5 4x4 | 3x3 Table 2. Material Handling Trips between Machines Machine 1 2 3 4 1 - 795 25 - 46 3 68 - 4 4 942- Table 3. Cost of Material Handling Trips between Machines Machine 1 2 3 4 |- 225 24 1 - 3 233