• The cost of operating a jet-powered commercial airplane varies as the three-halves (3/2) power of its velocity; specifically, C O =knv 3/2 , where n is the trip length in miles, k is a constant of proportionality, and v is velocity in miles per hour. It is know that at 400 miles per hour the average cost of operation is $300 per mile. The company that owns the aircraft wants to minimize the cost of operation, but that cost must be balanced against the cost of the passengers’ time (C C ), which has been set at $300,000 per hour. • (a) at what velocity should the trip be planned to minimize the total cost, which is the sum of the cost of operating the airplane and the cost of passengers’ time? • (b) How do you know that your answer for the problem in Part (a) minimizes the total cost?