The hedging problem is to find the face amount of each of the key rate securities such that the net key rate '01s of the overall position are all zero. Let’s denote $X_i$ as the face amount of hedging bond i that we need to sell.

We have following equation

(1) $X_1 \times \frac{0.0175}{100} + X_2 \times \frac{0.0099}{100} + X_3 \times \frac{0.0232}{100} - 80.4895 = 0$
$\Rightarrow 0.0175X_1 + 0.0099X_2 + 0.0232X_3 - 8048.95 = 0$

(2) $X_2 \times \frac{0.0250}{100} + X_3 \times \frac{0.0314}{100} - 193.4292 = 0$
$\Rightarrow 0.0250X_2 + 0.0314X_3 - 19342.92 = 0$

(3) $X_3 \times \frac{0.0487}{100} - 300 = 0$
$\Rightarrow 0.0487X_3 = 300$

From (3): $X_3 = \text{USD } 616,016.4271$
From (2) and (3): $X_2 = \text{USD } 0$
From (1), (2) and (3): $X_1 = -\text{USD } 356,721.7776$