$1.($a$)$ Using Mesh analysis, determine the currents i$\_($I$)$ and i$\_(2)$ of the circuit in Figure $1\mathrm{.}1.$ Hence, determine the power supplied by the current source.

Figure $1\mathrm{.}1$

$($b$)$ Find the Thevenin equivalent of the terminal a$,$b of the circuit in Figure $1\mathrm{.}2.$ If a resistor is connected to the terminals a$,$b$,$ determine the maximum power that can be delivered to the resistor.