  The Bomber Problem concerns optimal sequential allocation of partially
effective ammunition $x$ while under attack from enemies arriving according to
a Poisson process over a time interval of length $t$. In the doubly-continuous
setting, in certain regions of $(x,t)$-space we are able to solve the integral
equation defining the optimal survival probability and find the optimal
allocation function $K(x,t)$ exactly in these regions. As a consequence, we
complete the proof of the "spend-it-all" conjecture of Bartroff et al. (2010b)
which gives the boundary of the region where $K(x,t)=x$.
