An electronic device consists of three components. The three components are in series so that the failure of one component causes the failure of the device. The reliability (probability of no failure) of the device can be improved by installing one or two standby units in each component. The following table charts the reliability, r, and the cost, c. The total capital available for the construction of the device is $10,000. How should the device be constructed? (Hint: The objective is to maximize the reliability, , of the device. This means that the decomposition of the objective function is multiplicative rather than additive.)
No. of parallel Component 1 Component 2 Component 3
units ($) ($) ($)
1 .6 1000 .7 3000 .5 2000
2 .8 2000 .8 5000 .7 4000
3 .9 3000 .9 6000 .9 5000