Emily, a US tourist, is travelling to Canada and Mexico with a budget of $$2,000$ USD. She plans to exchange her money initially into Canadian Dollars $($CAD$)$ and then convert some of it to Mexican Pesos $($MXN$).$ The exchange rates at the time of her trip are:

$1$ USD $=1\mathrm{.}25$ CAD

$1$ CAD $=16$ MXN

Emily will spend $5$ days in Canada and $5$ days in Mexico. Her estimated daily expenditures are:

Canada: $150$ CAD per day

Mexico: $2,000$ MXN per day

However, there are fluctuations in exchange rates and transaction fees:

Just before she leaves, the USD to CAD rate changes to $1$ USD $=1\mathrm{.}20$ CAD.

The transaction fee for exchanging USD to CAD is $2\%.$

The transaction fee for exchanging CAD to MXN is $1\mathrm{.}5\%.$

The direct exchange rate for USD to MXN is $1$ USD $=19$ MXN with a $3\%$ transaction fee.

Additionally, her daily expenditures vary as follows:

In Canada: CAD $200$ on the first day and CAD $130$ on the last day. For the remaining three days, it is CAD $150$ per day.

In Mexico: MXN $2500$ on the first day and MXN $1800$ on the last day. For the remaining three days, it is MXN $2000$ per day.

Required:

a$)$ Calculate the total amount of money Emily will need in CAD and MXN for her trip with the fluctuating exchange rates and transaction fees. $(5$ marks$)$

b$)$ Determine the cost$-$effectiveness of two methods:

i$.$e

$1.$ Exchanging all her money directly into CAD first, then converting the required amount to MXN

OR

$2.$ Exchanging USD directly into CAD for her Canadian expenses and the remaining USD directly into MXN for her Mexican expenses. $(14$ marks$)$

c$)$ Identify the savings $($if any$)$ by comparing both methods. $(6$ marks$)$