Maple Syrup Co$.($MSC$),$ a Canadian syrup manufacturer, is expecting an inflow of $15$ million US$ in less than two months. Today's spot exchange rate is $1\mathrm{.}30$ CAD per US$$.$ MSC decides to hedge using options. The CAD interest rate is $4\mathrm{.}50\%.$ They contact the Royal Bank of Canada, which offers the following options on the US$:

American call option on the US$ with $T=3$ months, $K=1\mathrm{.}30$ CAD$/$US$$,$ and pric$C=0\mathrm{.}04$ CAD$/$US$

American put option on the US $ with $T=3$ months, $K=1\mathrm{.}30$ CAD$/$US $$,$ and price $P=0\mathrm{.}03$ CAD$/$US$

American call option on the US $ with $T=6$ months, $K=1\mathrm{.}30$ CAD$/$US$$,$ and price $C=0\mathrm{.}05$ CAD$/$US$

American put option on the US $ with $T=6$ months, $K=1\mathrm{.}30$ CAD$/$US $$,$ and price $P=0\mathrm{.}04$ CAD$/$US$

Assume that these options have no resale value and ignore transactions costs.

a$)$ Which option should MSC choose & why?

b$)$ What is the minimum value in CAD per US$ that MSC can establish in this hedge?

c$)$ Suppose that two months later $($i$.$e$.,$ at the time when MSC receives $15$ million US$$)$ the spot exchange rate is $1\mathrm{.}35$ CAD$/$US$$.$ What should MSC do$?$ How many CAD per US dollars will they get?

d$)$ Now, suppose that at the time MSC receives the $15$ fillion US$$,$ the spot exchange rate is $1\mathrm{.}28$ CAD$/$US$$.$ What should MSC do$?$ How many CAD per US dollars will they get?