You had the good luck to find a new oil field, which has a content of 10000 liters let us assume you have three time periods to extract the oil at the following prices per liter oil, where the subscipt indicates the periods: P1=$50, P2=$100, and P3=$150, let us assume that the interest rate is fixed to 10% per period. The extraction costs are $10 per liter.
1. What are the profit-maximizing extraction plan and the present value of the profit?
2. Now the situation has changed, the interest rates are given by r2=10% and r3=60%, what are now the optimal extraction plan and what is the present value of the profit?
3. The situation is the same as in 1, except that the extraction costs per liter are different every period and now they given by; c1=$10, c2=$20 and c3=$200. What are the optimal extraction plan and the present value of the profit?
4. The situation is like in 1, except P1=$50, P2=$55 and P3=$60.50. What are the optimal extraction plan and the present value of the profit?