$7\mathrm{.}4$ Suppose an AI character in a game can direct artillery fire onto a battlefield. The char$-$

acter wants to cause explosions that maximize enemy losses and minimize the risk to

friendly units. An explosion is modeled as a circle with a fixed deadly blast radius r$.$

Assuming the location of all enemy and friendly units is known, write down a function

that calculates the expected reward of an explosion at a $2$D location $($a$,$ y$).$