$1.$ Suppose you are given the following features of Bonds A$,$ B$,$ and C$.$

Price Yield Coupon rate Face Maturity

Bond A $$893\mathrm{.}7614\mathrm{.}166\%2\mathrm{.}400\%$ $$1,0001$

Bond B $$932\mathrm{.}449\mathrm{.}965\%2\mathrm{.}700\%$ $$1,0001$

Bond C $$820\mathrm{.}5722\mathrm{.}877\%1\mathrm{.}800\%$ $$1,0001$

$1$a$.$ If you want to create a synthetic version of Bond C$,$ how many units of Bond A and Bond B would you have to buy $($positive quantities$)$ and$/$or sell $($negative quantities$)?$

Quantity of A $=$

Quantity of B $=$

$1$b$.$ What is the arbitrage$-$free price of Bond C$?$

$1$c$.$ The arbitrage$-$free price of Bond C differs from the actual price of Bond C$.$ To exploit this arbitrage opportunity, should you:

Buy or sell Bond A$?$

Buy or sell Bond B$?$

Buy or sell Bond C$?$