Find subsequence of maximal length simultaneously satisfying two ordering constraints
A dynamic programming solution would work here, if the vitamin contents come from a finite set (for instance, bounded integers).
First, sort the fruits on price ascending and in the cases were two or more fruit have the same price, sort them on vitamin content (descending). 
Now, define $M[f, v]$ to be the maximal number of fruits in a sublist, containing only the last $f$ fruits (of the sorted list), having a vitamin content of at most $v$. $M[0, *] = 0$ and
$$M[f, v] = \begin{cases}
 \mathrm{max} \{M[f-1, v], 1 + M[f-1, V_f]\} &amp; \text{if \(V_f &lt;= v\)} \\
 M[f-1, v] &amp; \text{otherwise} \\
\end{cases}$$
Using dynamic programming gives you a solution that runs in $O(\text{number of fruit} \times \text{possible vitamin values})$.