ANSWER USING KNAPSACK WITH ALTERNATIVE STATES AND RECURSIVE EQUATIONS

Consider an electronic system consisting of four components, each of which must work for the system to function. The reliability of the system can be improved by installing several parallel units in one or more of the components. The following table gives the probability that the respective components (labeled as Comp. 1, 2, 3, and 4) will function if they consist of one, two, or three parallel units: Parallel Units Probability of Functioning Comp. 1 Comp. 2 Comp. 3 Comp. 4 0.5 0.6 0.7 0.5 0.7 0.8 0.8 0.8 0.9 0.9 1 2 3 0.6 0.7 The probability that the system will function is the product of the probabilities that the respective components will function. The cost (in hundreds of dollars) of installing one, two, or three parallel units in the respective components (labeled as Comp. 1, 2, 3, and 4) is given by the following table: Parallel Units Cost Comp. 1 Comp. 2 Comp. 3 1 2 1 2 4 3 3 5 4 1 2 3 Comp. 4 2 3 4 Because of budget limitations, a maximum of $1,000 can be expended. Use dynamic programming to determine how many parallel units should be installed in each of the four components to maximize the probability that the system will function