Lucie likes consuming candy (c) and fruit (f), and dislikes consuming plastic packaging (p), and has rational preferences over bundles (c, f, p). No matter how many units of each good she has, Lucie is always willing to exchange one piece of fruit for one piece of candy (and vise versa), and always has to be compensated by an extra piece of fruit for every piece of plastic packaging she has to consume.

Are her preferences strictly convex? If you answer yes, explain briefly (no need for a formal proof). If you answer no, provide a counterexample.