A system consists of 3 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:

Subsystem, i Wi (lb) Reliability, ri 1 4 0.96 2 2 0.92 3 6 0.98

The reliability of the subsystem i is given by Ri = 1- (1-ri)^ni, i =1,2,3, where ni 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 atleast one and not more than 3 components ib any subsystem. The total payload is restricted to 20 lb. Use DYNAMIC PROGRAMMING to find the number of components to be used in the 3 subsystems to maximize the overall reliability of the system.

Components of type 1 Subsystem 1 Components of type 2 Subsystem 2 Components of type 3 Subsystem 3 Components of type 1 Subsystem 1 Components of type 2 Subsystem 2 Components of type 3 Subsystem 3