An oil company has 6 units of money available for exploration of three sites. If oil is present at a site, the probability of finding it is a function of the funds allocated for exploring the site, as shown in the table.
The probably that oil exists at the sites 1, 2, and 3, are 0.2, 0.4, and 0.5, respectively. Using a dynamic-programming approach, determine how much money should be allocated to exploration of each site to maximize the probability of discovering oil. Treat this as a three-stage process, in which stage j is allocation of money to site j. Use the following definitions:
= number of units of money allocated to site j
= probability of finding oil at site j when is allocated, given that oil exists
= probability that oil exists at site j
u = number of units of money remaining
= minimum probability of not finding oil, given that the company is in state u at the start of stage j