Answer
$P^{*}= 634$ kPa
Work Step by Step
The lowest pressure that can be obtained at the throat is the critical pressure $P^*$, which is determined from
$$
P^*=P_0\left(\frac{2}{k+1}\right)^{k /(k-1)}=(1200 \mathrm{kPa})\left(\frac{2}{1.4+1}\right)^{1.4 /(1.4-1)}\\=634 \mathrm{kPa}
$$
