Question 2 : Modeling with networks [ 20 points ] Fred has $2 200 to invest over the next five years . At the beginning of each year he can invest money in one - year or two- year time deposits . The bank pays 8 percent interest on one-year time deposits and 17 percent ( total ) on two- year time deposits . In addition , West World Limited will offer three - year certificates starting at the beginning of the second year . These certificates will return 27 percent ( total ) . To fix ideas , if Fred invests $ 1 in a one- year deposit at the beginning of the first year , a two - year deposit at the beginning of the second year and a two-year deposit at the beginning of the forth year , he will have $1 X 1 . 08 x 1. 17 X 1. 17 = $1. 478 at the end of the fifth year . Whenever money is available for investment in a particular year , Fred chooses exactly one investment option to reinvest it all . He would like to find an investment plan that will maximize the amount of money he has at the end of the 5 th ( beginning of the 6th ) year . Model this problem as a shortest path problem . ( To answer this question , it is sufficient to represent the network arcs , vertices and arc costs , and to identify the source and sink of the shortest path problem ) . Hint : Recall that In ( a * 1 bacz ) = 20 1 In ( a ) + 202 In ( 6 )