Suppose we have N stages to construct I successful components se- quentially. At each stage we allocate a certain amount of money for the construction of a component. If y (y [0, Y ]) is the amount allocated, then the component constructed will be a success with probability P (y), where P is a continuous nondecreasing function satisfying P (0) = 0. After each com- ponent is constructed, we are informed whether or not it is successful. If, at the end of the N stages, we are j components short, then a final penalty cost C(j) is incurred. Formulate this problem as a finite horizon Markov Decision Process