Consider a directed communications network, where each arc represents the communication link between

two geographically distant points. Each communication link between points i and $j$ has a probability

of failure of $p_{ij}.$ Then, for any path through the network, the probability of that particular path being

operative is the product of the probabilities $(1-p_{ij})(1-p_{jk})(1-p_{kl})dots$ of the communication links

connecting the two points of interest.

a$)$ Formulate a network model to determine the path from $s$ to $t$ having the highest probability of being

operative.

b$)$ In what class does the problem formulated in $($a$)$ fall?

c$)$ How can this formulation be transformed into a network problem?