Define the objective function.

Step 1: Define the objective function.
Let $P_i(x_i)$ be the probability of finding oil at site $i$ given $x_i$ units of money are allocated to it, assuming oil exists at site $i$. These values are given in the table.
Let $p_i$ be the probability that oil exists at site $i$.
$p_1 = 0.4$
$p_2 = 0.3$
$p_3 = 0.2$

The probability of finding oil at site $i$ given an allocation $x_i$ is $p_i \times P_i(x_i)$.
The probability of not finding oil at site $i$ given an