Suppose you observe the following exchange rates: $1=$ $$0\mathrm{.}85$; $1=$ $$1\mathrm{.}60$; $2\mathrm{.}00=1\mathrm{.}00.$Which of the following transactions will make money?

a$.$

Start with dollars, exchange for euros at $1=$ $$0\mathrm{.}85$; then exchange for pounds at $2\mathrm{.}00=1\mathrm{.}00$; and finally exchange for dollars at $1=$ $$1\mathrm{.}60.$

b$.$

Start with dollars, exchange for pounds at $1=$ $$1\mathrm{.}60,$ then exchange for euros at $2=1\mathrm{.}00,$ and finally exchange for dollars at $1=$ $$0\mathrm{.}85.$

c$.$

Start with pound; exchange for dollars $1=$ $$1\mathrm{.}60$; then exchange for euros $1=$$$0\mathrm{.}85$; and finally exchange for pounds $2\mathrm{.}00=1\mathrm{.}00.$

d$.$

Start with euros; exchange for pounds $2\mathrm{.}00=1\mathrm{.}00$; then exchange for dollars $1=$ $$1\mathrm{.}60$; and finally exchange for euros $1=$$$0\mathrm{.}85.$