Question 1: (35 points A manufacturing process is represented by the following block diagram: G1s R(S) C(s) G28 G5(s G6(s) G3(8) G4(s) G75 (a) [15 points) Reduce the following block diagram to its most simplified form and find C(s)/R(s). (b) (5 points) If G; (s) = 5, G2(s) = 5, Gz(s) = 4, G4(s) = 4s, Gs(s) = 1, G.(s) = 2s , and Gy(s) = 3s, then determine the transfer function C(s)/R(s). (e) [5 points) If the input is r(t) = 2 ut). Determine the output c (ttoo) when time goes to infinity using the final value theorem. (d) [10 points] Explain, by your own words, the reason why we need to reduce the block diagram as explained in our lectures