1 At the beginning of year 1, Sunco Oil owns i0 barrels of oil reserves. During year t(t  1, 2, . . . , 10), the following events occur in the order listed: (1) Sunco extracts and refines x barrels of oil reserves and incurs a cost c(x): (2)

Sunco sells year t’s extracted and refined oil at a price of pt dollars per barrel; and (3) exploration for new reserves results in a discovery of bt barrels of new reserves.

Sunco wants to maximize sales revenues less costs over the next 10 years. Formulate a dynamic programming recursion that will help Sunco accomplish its goal. If Sunco felt that cash flows in later years should be discounted, how should the formulation be modified?