Assignment:
For a computer to work properly, three subsystems of the computer must all function properly. To increase the reliability of the computer, spare units may be added to each system. It costs $100 to add a spare unit to system 1, $300 to system 2, and $200 to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in the following table:
Number of Probability that a system works
Spares System 1 System 2 System 3
0 .85 .60 .70
1 .90 .85 .90
2 .95 .95 .98
Use dynamic programming to maximize the probability that the computer will work properly, given that $600 is available for spare units.
Provide complete and step by step solution for the question and show calculations and use formulas.