Bob lives on an island and has 20 apple trees in the current period. Which currently produces 180 apples. Bob sells apples to neighboring islands to make living. Bob can borrow and lend apples with neighboring island. In the apple credit market, a loan of 1 apple must be repaid with 2 apples in the future period. In each period, Bob's apple trees produce apples and then 10% of them die. If Bob plants an apple in the current period, it will grow into a productive apple tree in the future period. At the end of the future period, Bob can sell any remaining apple tree for 1 apple each. The diminishing marginal product applies. Therefore, the output in the future period, for given number of trees in production in the future period is given in the following table.

Future Trees Future Output

15 155.0

16 162.0

17 168.0

18 173.0

19 177.0

20 180.0

21 182.0

22 183.8

23 184.8

24 185.2

25 185.4

What is Bob's optimal quantity of investment?