2. Suppose that a system of components features four subsystems. Subsystem 1 consists of 1 component. Sub- system 2 consists of two identical components arranged in parallel. Subsystem 3 consists of three identical components arranged in parallel. Subsystem 4 consists of two identical components arranged in parallel. These four subsystems are then arranged in series. Let Ri denote the reliability of the component used in Subsystem 1, R2 the reliability of the component used in Subsystem 2, R3 the reliability of the component used in Subsystem 3, and R4 the reliability of the component used in Subsystem 4. Before beginning this question, you should draw a picture of the system to help you answer the following questions (you do not need to submit this picture in your assignment). (e) Now suppose that components are available with reliabilities 0.5, 0.6, 0.7, 0.8 and 0.9. The cost of a component with 50% reliability is $500 and each 10% increase in reliability costs $100. Therefore, the Cost function of Subsystem 1 in terms of R can be written down as C1 = 500 + 100(R1 - 0.5)/0.1. Write down the Cost functions for each of the following, denoting them C2, C3 and C4 respectively: The cost of Subsystem 2 in terms of R2 The cost of Subsystem 3 in terms of R3 The cost of Subsystem 4 in terms of RA (f) Let C denote the cost of the entire system. Write down the Cost function of C in terms of C1, C2, C3 and C4. (h) Suppose the reliability of the system must be at least 0.65 and that the different subsystems can contain identical component types if desired. Your friend suggests a new design whereby the four subsystems are still arranged in series, but now each of the four subsystems only consist of 1 component. Do you think your friend's design is feasible and/or preferable over the original design? Explain your reasoning clearly