GENERAL STRATEGY:

corey loads up with the max amount of bananas, (1000)

travels 1 miles, (999)

dumps all but one banana (998)

uses that banana to return to the stockpile

and repeats until the stock pile is empty

STAGE 1

corey has more than 2000 bananas

each mile costs 5 bananas 3 forward trips and 2 reverse trips

so corey reaches the 200 mile mark with 2000 banans left

Stage 2

corey has between 1000 and 2000 bananas

each mile now costs 3 bananas 2 forward trips and 1 reverse trip

so corey traves a furter 333+1/3 miles (total 533+1/3) with 1000 banans left

stage 3

corey has 1000 or less bananas

each mile now costs only 1 banana, 1 forward trip only

corey travels the last 467+2/3 miles costing 467+2/3 bananas

corey has traveled 1000 miles with 533+1/3 bananas left