Estimating a cost function, high-low method. Reisen Travel offers helicopter service from suburban
towns to John F. Kennedy International Airport in New York City. Each of its 10 helicopters makes
between 1,000 and 2,000 round-trips per year. The records indicate that a helicopter that has made 1,000
round-trips in the year incurs an average operating cost of $300 per round-trip, and one that has made 2,000
round-trips in the year incurs an average operating cost of $250 per round-trip.
1. Using the high-low method, estimate the linear relationship y = a + bX, where y is the total annual operating
cost of a helicopter and X is the number of round-trips it makes to JFK airport during the year.
2. Give examples of costs that would be included in a and in b.
3. If Reisen Travel expects each helicopter to make, on average, 1,200 round-trips in the coming year,
what should its estimated operating budget for the helicopter fleet be?
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To estimate the cost function using the high-low method, we need to find the values of a and b in the linear equation y = a + bX, where y is the total annual operating cost of a helicopter and X is the number of round-trips it makes to JFK airport during the year.
1. To start, we need to identify the highest and lowest levels of activity and the corresponding costs. From the given information, we know that when a helicopter makes 1,000 round-trips, the average operating cost is $300 per round-trip. Let's designate this as our low point: (X1, y1) = (1000, 300). Similarly, when a helicopter makes 2,000 round-trips, the average operating cost is $250 per round-trip. This will be our high point: (X2, y2) = (2000, 250).
2. Now, we can calculate the slope of the line, which represents the variable cost per round-trip:
b = (y2 - y1) / (X2 - X1)
= (250 - 300) / (2000 - 1000)
= -50 / 1000
= -0.05
So, b represents the variable cost per round-trip, which is -$0.05.
Next, we substitute one of the points (X1, y1 or X2, y2) and the slope into the equation to find the value of a:
a = y - bX
a = y1 - bX1
a = 300 - (-0.05 * 1000)
a = 300 + 50
a = 350
Therefore, a represents the fixed cost component, which is $350 in this case.
The estimated cost function is y = 350 - 0.05X.
3. To calculate the estimated operating budget for the helicopter fleet, we substitute the average number of round-trips expected (1,200) into the cost function:
Estimated operating budget = y = 350 - 0.05 * 1,200
= 350 - 60
= 290
Therefore, the estimated operating budget for the helicopter fleet would be $290 or $290,000.
Examples of costs included in a (fixed cost component):
- Depreciation of helicopter assets
- Administrative and office expenses
- Rent or lease expenses for hangar space
- Insurance premiums for the fleet
Examples of costs included in b (variable cost per round-trip):
- Fuel costs
- Pilot salaries and benefits
- Maintenance and repair expenses
- Landing fees and airport charges