A ship carries cargo back and forth between two ports. In each period t, a quantity qt of cargo arrives at port 1 to be shipped to port 2, and quantity q i of cargo arrives at port 2 to be shipped in...

A ship carries cargo back and forth between two ports. In each period

t, a quantity qt of cargo arrives at port 1 to be shipped to port 2, and quantity

q

i of cargo arrives at port 2 to be shipped in the opposite direction. The unit

cost of holding cargo at either port is ct in period t. At the beginning of each

period, the ship captain decides whether to sail to the other port at a cost

of C, or to wait for more cargo to accumulate before sailing. The capacity

of the ship is infinite for practical purposes. Write a dynamic programming

recursion to find a minimum-cost sailing schedule.