Problem
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 cost of operating the ship and the cost of perishable cargo?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.