1. An electronic system consists of three components, each of which must function in order for the system to function. The reliability of the system (probability of successful performance of the system) can be improved by installing several stand-by units for one or more of the components. The reliability of the system is given by the product of each component, while the reliability of each component is a function of the number of stand- by units as given below:
Number of
STAND - BY Re liability of Component
Units1 2 3
0 0.5
1 0.6
2 0.7
3 0.8
4 0.9
5 1.0
0.6 0.7 0.75 0.9 0.95 1.0 1.0 1.0 1.0 1.0 1.0 1.0
For instance, if no stand-by unit is provided, the reliability of component 2 is 0.6; with 2 stand-by units, its reliability increases to 0.95. The cost and weight of each stand-by unit for the three components are as follows:
UnitCost Weight/Unit Component ($) ( Kg )
1 20 2 2 30 4 3 40 6
We have a budget restriction of $150 and a weight restriction of 20 kg for all the stand-by units. The problem is to determine how many stand-by units should be installed for each of the three components so as to maximize the total reliability of the system. Formulate this as a linear integer program. Do not solve.