Let ~g_i~ be a field or a strip. Denote by ~n_i~ the number of cypresses in a field or a strip. If we denote by ~e_i~ the number of olive trees in a ~g_i~, we have: ~e_i = n_i~ if ~g_i~ is a field or ~e_i = n_i-1~ if ~g_i~ is a strip.

Consider now the following KNAPSACK problem: ~\max \sum_{i=1}^{n+m} e_i x_i~, such that ~\sum_{i=1}^{n+m} n_i x_i \le Q~ and ~x_i \in \{0, 1\}~, where ~n, m~ are the numbers of fields and strips respectively.

An optimum solution ~x^*_i~, ~1 \le i \le n+m~, of this problem consists of a subset of ~g_i~ such that the total number of their cypresses is at most ~Q~ and the total number of the included olive trees is maximized. However in general ~Q' = \sum_{i=1}^{n+m} n_i x_i < Q~. If this is the case, then there is some ~g_i~ such that ~x^*_i = 0~ and ~n_i > Q-Q'~, for otherwise the optimum solution can be improved by the inclusion of ~g_i~, a contradiction. Therefore, adding a chain of ~Q-Q'~ cypresses of ~g_i~ and its ~Q-Q'-1~ olive trees to the optimum solution of the knapsack problem above, yields an optimum solution. The KNAPSACK problem can be solved optimally in ~\mathcal O((n+m)Q)~ time by a Dynamic Programming algorithm.