Estimating a cost function, high-low method?
Reisen Travel offers helicopter service from suburban towns to john F. Kennedy Airport. Each of it's 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 has an average operating cost of $300, and one that has made 2,000 round trips has an average operating cost of $250.
1. Estimate the linear relationship y = a+bx, where y is the total annual operating cost of the helicopter and x is the number of round trips.
2. give examples of costs that would be included in a and b
3. if Reisen Travel expects each helicopter to make an aver 1,200 round trips in the comming year, what should its operating budget for the helicopter fleet be?
1. The high-low method is a simple technique used to estimate a cost function based on two data points - the highest and lowest levels of activity. In this case, we have the average operating costs for helicopters that have made 1,000 and 2,000 round trips.
To estimate the linear relationship between the number of round trips (x) and the total annual operating cost (y), we can use the high-low method as follows:
- Determine the difference in operating costs between the high and low levels of activity: $300 - $250 = $50.
- Determine the difference in round trips between the high and low levels of activity: 2,000 - 1,000 = 1,000.
- Calculate the variable cost per round trip (b): $50 / 1,000 = $0.05.
- Calculate the fixed cost component (a): To do this, we can use one of the data points (either the high or low) and substitute the values into the equation: y = a + bx. Let's use the low level of activity (1,000 round trips) and its corresponding average operating cost ($300).
$300 = a + ($0.05 x 1,000)
$300 = a + $50
a = $300 - $50
a = $250.
So, the estimated linear relationship is: y = $250 + $0.05x, where y is the total annual operating cost and x is the number of round trips.
2. In this cost function, 'a' represents the fixed cost component, which includes costs that are incurred regardless of the level of activity. In the context of Reisen Travel's helicopter service, examples of costs that would be included in 'a' are:
- Depreciation and maintenance of helicopters (annual costs)
- Administrative and management expenses (e.g., salaries, office rent)
On the other hand, 'b' represents the variable cost per round trip, which includes costs that vary with the level of activity. Examples of costs that would be included in 'b' are:
- Fuel expenses (which increase as the number of round trips increases)
- Pilot and crew wages (costs increase with more round trips)
3. If Reisen Travel expects each helicopter to make an average of 1,200 round trips in the coming year, we can use the estimated cost function (y = $250 + $0.05x) to calculate the expected operating budget for the helicopter fleet:
Operating budget = Total annual operating cost per helicopter x Number of helicopters
Operating budget = ([$250 + ($0.05 x 1,200)] x 10)
Calculating:
Operating budget = ($250 + $60) x 10
Operating budget = $310 x 10
Operating budget = $3,100
Therefore, Reisen Travel's operating budget for the helicopter fleet in the coming year should be $3,100.