Since the conditional optimization of 1, 2, 3 and 4th steps already performed in Table. 3, then left the table to finish the implementation of constrained optimization on the 0-th step, and only for g_i = 200. The above calculations are made in the Table. 5. Optimization of 0-th step during unconstrained optimization we Zmax = Z0 * (200) = 27. The maximum is reached at two optimal controls x0 = 40 and O = £ 80. Having taken the first option, we consistently £ 0 * = li *-x0 * = 200-40 = 160 and * i * = 40 (from Table. 2). Furthermore, gi * = 160-40 = 120, of Table. 2, we get x2 = 80 (or 40). Again find £ 2 = 120-80 = 40 (or% = 120-40 = 80) and respectively x3 = 0 (or x 3 = 40). Finally, | 3 = 40-0 = 40 (or 80-40 = 40) and x4 = 40. Thus, we get two alternative optimal control f / i * = (40, 40, 80, 0, 40) and t / 2 * == (40, 40, 40, 40, 40). Similarly, selecting the 0-th step of £ 0 = 80, we get a third alternative optimal control t / 3 = (80, 40, 40, 0, 40).
What conditions need to meet the overall objective of optimization, so it can be described by the model DP? These conditions are:
1. The task can be interpreted as /?-Step process control and process performance indicator can be represented in an additive form, ie, the sum of the performance at each step.
2. Structure of the problem is invariant with respect to the number of steps n, ie, must be defined for any n, and not to depend on this number.
3. At each step the state of the system is determined by a finite number five of the state and is controlled by a finite number r control variables, and 5 and g do not depend on the number of steps n
4. Selection of control on the k-th step does not affect the previous steps, and the state at the beginning of this step is a function of the previous state and the selected control on it (no-effect).

Note that the implementation of these conditions is sometimes obvious, sometimes reached after appropriate transformation.