Problem $4($Required$,25$ marks$)$ A company is facing $3$ liabilities recently. It needs to repay $\backslash ($ L$\_\{1\}=10404,$ L$\_\{2\}=23813\mathrm{.}5\backslash ),\backslash ($ L$\_\{3\}=20676\mathrm{.}342\backslash )$ after $2$ years, $4$ years and $7$ years respectively. The term structure is currently flat and the annual effective interest rate is currently $\backslash ($ i$\_\{0\}=2\backslash \%\backslash )$ To fulfill the liability, the company decides to adopt some immunization strategies using the following $3$ bonds: $-$ Bond A: $3$ years zero coupon bond $-$ Bond B: $5$ years zero coupon bond $-$ Bond C: $8$ years zero coupon bond The company would like to construct a bond portfolio which can fulfill the liability against a small change in interest rate in future. Among the immunization strategies discussed in the lecture, which strategies will be effective? Explain your answer. $(*$Note: You need to discuss the feasibility of each of the immunization strategy. If the strategy is feasible, please determine all possible portfolios that can achieve the goal$)$