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?

1. The high-low method is used to estimate a cost function by using the highest and lowest values of the independent variable (X) and corresponding costs (y). In this case, the highest value is 2,000 round-trips with an average cost of $250 per round-trip, and the lowest value is 1,000 round-trips with an average cost of $300 per round-trip.

To estimate the linear relationship, we need to calculate the slope (b) and the intercept (a) of the cost function equation y = a + bX.

First, we calculate the change in costs (Δy) and the change in round-trips (ΔX):
Δy = $250 - $300 = -$50
ΔX = 2,000 - 1,000 = 1,000

Next, we calculate the slope (b) by dividing the change in costs by the change in round-trips:
b = Δy / ΔX = -$50 / 1,000 = -$0.05

Now, we can calculate the intercept (a) using the formula:
a = y - bX
Using the average cost and round-trips of either of the given data points:
a = $300 - (-$0.05 * 1,000) = $350

Therefore, the estimated linear relationship is y = $350 - $0.05X.

2. In the cost function, a represents the fixed costs, which are the costs that do not change with the level of round-trips, such as the cost of maintaining the helicopters, insurance, salaries of the staff, rental fees for the helicopter base, etc. These costs are incurred even if no round-trips are made.

On the other hand, b represents the variable costs per round-trip, which vary with the level of round-trips made. These costs can include fuel costs, maintenance and repair costs specific to each round-trip, landing fees, etc.

3. If Reisen Travel expects each helicopter to make, on average, 1,200 round-trips in the coming year, we can use the estimated cost function to calculate the operating budget for the helicopter fleet.

Substituting the value of X = 1,200 into the cost function equation y = $350 - $0.05X:
y = $350 - $0.05 * 1,200
y = $350 - $60
y = $290

Therefore, the estimated operating budget for the helicopter fleet would be $290 for each helicopter, assuming an average of 1,200 round-trips. To get the total operating budget, you would multiply this cost by the number of helicopters in the fleet.