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The calculation of how many servers can be installed in a data centre was made easier by the introduction of a standardised floor tile, which is a square that is 2 ft by 2 ft, occupying 4 square feet of floor area. Two facing rows of servers can either fit in a '7-tile pitch' (if a 3 ft by 2 ft rack is used) or an 8-tile pitch' (if a 4 ft by 2 ft rack is used). In either case, there must be one unoccupied tile width around the outside of the racks and two tiles between the rows. Here is an illustration of the ground plan for a cluster of servers in a 7-tile pitch and for a cluster of servers in an 8-tile pitch. In each case, there are four racks of servers in each row. rack rack rack rack rack rack rack rack 2 ft 3 ft Figure 1 7-tile pitch (for 3 ft by 2 ft racks in rows of four) rack rack rack rack rack rack rack rack 2 ft Figure 2 8-tile pitch (for 4 ft by 2 ft servers in rows of four) a. The ratio of occupied tiles to the total number of tiles in the 8-tile pitch shown in Figure 2 is : i. Find the equivalent ratio for the cluster of racks shown in Figure 1. ii. The general expression for the ratio of occupied tiles to the total tiles in an 8-tile pitch, if each row contains n racks is: n 2(n+2) Find the general expression for the ratio of occupied tiles to the total tiles in a 7-tile cluster if there are n racks in each row - check that when n = 4, your expression gives the same answer as you wrote down in (a)(i)