Answer
See below.
Work Step by Step
Let $x$ be the number of small boxes, $y$ be the number of medium boxes, $z$ be the amount of large boxes. Then our equations:
(for oatmeal raisin): $x+2y+2z=15$
(for chocolate chip): $x+y+2z=10$
(for shortbread): $y+3z=11$
Deducing the second equation from the first one we get: $y=5$, then substituting this into the third, $z=2$, then $x=1$. So we buy $1$ small, $5$ medium and $2$ big boxes.
