2-26. The cost of operating a large ship (CO) varies as
the square of its velocity (v); specifically, CO = knv2,
where n is the trip length in miles and k is a constant of
proportionality. It is known that at 12 miles/hour the
average cost of operation is $100 per mile. The owner of
the ship wants to minimize the cost of operation, but
it must be balanced against the cost of the perishable
cargo (Cc), which the customer has set at $1,500 per
hour. At what velocity should the trip be planned to
minimize the total cost (CT), which is the sum of the
PROBLEMS 57
cost of operating the ship and the cost of perishable
cargo? (2.3)