Solve using dynamic programming method of reliability improvement problem

To solve this problem using dynamic programming, we want to maximize the probability of finding oil at at least one site. This is equivalent to minimizing the probability of finding no oil at any site.

Let $p_i$ be the prior probability that oil exists at site $i$.
$p_1 = 0.4$, $p_2 = 0.3$, $p_3 = 0.2$.

Let $P_i(x_i)$ be the conditional probability of finding oil at site $i$ given $x_i$ units are allocated to it and oil exists at site $i$. These values are given in the table.

The probability of finding oil at site $i$ with allocation $x_i$ is $p_i \