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?
please can i hlep me
1. To estimate the linear relationship using the high-low method, we need to find the slope (b) and the intercept (a) of the cost function.
Step 1: Identify the high and low data points:
The high data point is when a helicopter has made 2,000 round-trips and incurs an average operating cost of $250 per round-trip.
The low data point is when a helicopter has made 1,000 round-trips and incurs an average operating cost of $300 per round-trip.
Step 2: Calculate the slope (b):
We can calculate the slope using the formula:
b = (Cost at High Point - Cost at Low Point) / (Round-Trips at High Point - Round-Trips at Low Point)
b = ($250 - $300) / (2,000 - 1,000)
b = -$50 / 1,000
b = -0.05
Step 3: Calculate the intercept (a):
To find the intercept, we can use the formula:
a = Cost at Low Point - (b * Round-Trips at Low Point)
a = $300 - (-0.05 * 1,000)
a = $300 + $50
a = $350
So, the estimated linear relationship is:
y = $350 - $0.05X
2. In this context, the cost function can be represented as:
a: Fixed Costs - Costs that are incurred regardless of the number of round-trips. For example, maintenance expenses, insurance, administrative costs, etc.
b: Variable Costs per unit - Costs that change based on the number of round-trips. For example, fuel costs, pilot salaries, 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 fleet.
Substitute X = 1,200 into the cost function:
y = $350 - $0.05(1,200)
y = $350 - $60
y = $290
Therefore, the estimated operating budget for the helicopter fleet would be $290 per round-trip multiplied by the average number of round-trips (1,200):
Estimated Operating Budget = $290 * 1,200
Estimated Operating Budget = $348,000.
To estimate the cost function using the high-low method, we need to determine the fixed cost (a) and the variable cost per round-trip (b).
1. To find the fixed cost (a), we can use the high and low cost observations. In this case, the high cost is $250 per round-trip (2,000 trips) and the low cost is $300 per round-trip (1,000 trips).
First, calculate the change in cost (Δy) and the change in round-trips (ΔX):
Δy = $250 - $300 = -$50
ΔX = 2,000 - 1,000 = 1,000
Next, calculate the variable cost per round-trip (b):
b = Δy / ΔX = -$50 / 1,000 = -$0.05
Now that we have the variable cost per round-trip (b), we can find the fixed cost (a) by substituting the values of one observation (either high or low cost) into the cost function:
Using the low cost values: $300 = a + (-$0.05) * 1,000
Simplifying the equation: a = $300 + $50 = $350
Therefore, the cost function (y) can be estimated as: y = $350 - $0.05X
2. In the cost function, 'a' represents the fixed costs that are incurred regardless of the number of round-trips made. This could include expenses such as helicopter maintenance, advertising, insurance, and salaries.
The variable cost per round-trip (b) represents the costs that vary with the number of trips made. This could include expenses like fuel, landing fees, and temporary staffing.
3. If Reisen Travel expects each helicopter to make an average of 1,200 round-trips in the coming year, we can use this value (X = 1,200) to estimate the operating budget (y).
Using the estimated cost function: y = $350 - $0.05 * 1,200
Simplifying the equation: y = $350 - $60 = $290
Therefore, the estimated operating budget for the helicopter fleet would be $290,000.