11. On the label with the list of ingredients of a confectionery product, it can be read: sugar, palm oil, hazelnuts 14%, cocoa, milk $6 \%$. Knowing that the ingredients are listed in order (no ingredient can be present in a larger quantity than another listed before it), what is the maximum percentage of palm oil that the confectionery could contain?
(A) $21 \%$
(B) $14 \%$
(C) $80 \%$
(D) $40 \%$
(E) $37 \%$
Problem 11. The answer is (E).

Let's call $z, p, c$ the quantities of sugar, palm oil, and cocoa present in the product (expressed as a percentage). We know that $z+p+c=80$, and that $6 \leq c \leq 14 \leq p \leq z$. The maximum percentage of palm oil that the product could contain is obtained for the minimum values of $c, z$ of the other two ingredients, compatible with these equations and inequalities; that is, for $c=6$ and $z=p$. Therefore, $p=(80-6) / 2=37$.

(Problem proposed by F. Poloni)