Problem 3 Star$ lnc. uses a set of mediumhaul trucking rms to distribute its coee beans from Seattle to the cities in which its coee shops are located. Each shipment of beans may pass through several cities before reaching its nal destination, and on each leg of the journey there is a risk that the beans may spoil from improper temperature control or handling. Star$ would like to maximize the probability that its beans arrive unspoiled in Charlottesville. The probl can be modeled abst-ractly in terms of a directed network N = (V, E)} with node set V and are set E. In this network, each node '1: E V represents a city through which the beans may pass} and each are a E E represents a possible intercity shipping route. For each arc s E E , there is an associated real number p[e] that is the probability that the beans will survive unspoiled after shipment alng are 9.. Thus the probability that the beans arrive unspoiled is the product of the probabilities on the arcs in the path that the beans follow from Seattle to Charlottesville. Formulate the problem of maximizing the probability that the beans arrive unspoiled in Charlottesville as a shortest paths problem. (Hint: recall that for any positive numbers (1,5, we have log{eb} = logEo} + log[b].]