O2 (25%, DP): A system consists of three subsystems in series, with each subsystem consisting of several components in parallel, as shown in the figure below. The weights and reliabilities of the various components are given below Weight of each component, wi (lb) 4 Reliability of each component, ri 0.96 0.92 0.98 Subsystem, i The reliability of subsystem i is given by Ri 1- (1 - r)i 1,2,3, where n is the number of components connected in parallel in subsystem i, and the overall reliability of the system is given by Ro-R1R2R3. It was decided to use at least one and not more than three components in any subsystem. The system is to be transported into space by a space shuttle while the total payload is restricted to 20 lb. Use dynamic programming to find the number of components to be used in the three subsystems to maximize the overall reliability of the system. Components of type 1 Components of type 2 Components of type 3 n2 n3 Subsystem 1 Subsystem 2 Subsystem 3 O2 (25%, DP): A system consists of three subsystems in series, with each subsystem consisting of several components in parallel, as shown in the figure below. The weights and reliabilities of the various components are given below Weight of each component, wi (lb) 4 Reliability of each component, ri 0.96 0.92 0.98 Subsystem, i The reliability of subsystem i is given by Ri 1- (1 - r)i 1,2,3, where n is the number of components connected in parallel in subsystem i, and the overall reliability of the system is given by Ro-R1R2R3. It was decided to use at least one and not more than three components in any subsystem. The system is to be transported into space by a space shuttle while the total payload is restricted to 20 lb. Use dynamic programming to find the number of components to be used in the three subsystems to maximize the overall reliability of the system. Components of type 1 Components of type 2 Components of type 3 n2 n3 Subsystem 1 Subsystem 2 Subsystem 3